After some more readings and reflection, I think the answer is two-fold: state capitalism is both bigger and smaller than socialism.
It's bigger in the sense that it's more widespread, e.g. from Saudi Arabia to China. It's hard to find much ideological similarities between these two countries besides a (higher) level of authoritarianism (compared to the West). And from that it's also clear that state capitalism is also smaller than socialism in scope, in the sense that these countries don't try to have as much control over the economy as the former Eastern Bloc countries had in Soviet times.
And state capitalism is also older as a realization. The Economist points to the East India Company as historical precursor of the modern resurgence.
State-directed capitalism is not a new idea: witness the East India Company. But as our special report this week points out, it has undergone a dramatic revival. In the 1990s most state-owned companies were little more than government departments in emerging markets; the assumption was that, as the economy matured, the government would close or privatise them. Yet they show no signs of relinquishing the commanding heights, whether in major industries (the world's ten biggest oil-and-gas firms, measured by reserves, are all state-owned) or major markets (state-backed companies account for 80% of the value of China's stock market and 62% of Russia's). And they are on the offensive. Look at almost any new industry and a giant is emerging: China Mobile, for example, has 600m customers. State-backed firms accounted for a third of the emerging world's foreign direct investment in 2003-10.
And this may be a little more controversial, but some theorists argue that socialism never really existed, only different levels of state capitalism.
We do not doubt the sincere Marxist consciousness and anti-capitalist commitment of
the revolutionaries who inaugurated the USSR and PRC. However, notwithstanding
their battles to establish and defend socialism and to move toward communism, they
could not and did not install communist class structures as the prevailing social organization of production in either country. Instead, they established particular state forms of
capitalism and state forms of feudalism as means to improve their nations’ economic and
military strength and their citizens’ standards of living. Thus, by the second half of the
20th century, the dominant conflicts occurred among:
1) mostly private capitalisms (the US, Western Europe, Japan, etc.),
2) a state capitalism in the USSR and Eastern Europe, and
3) first a state feudalism and then a state capitalism in the PRC
They use the term "state capitalism" more narrowly than usual though (compared to the previous two sources) i.e. only when state officials appropriate most resources:
Lenin seemed to recognize the difference between class and power processes. For
example, not long after the 1917 Soviet revolution, he admitted that the state’s control
of production and distribution (and hence the surplus) was a ‘state capitalism’ but, he
argued, it was a step toward communism because state power was in the hands of workers (organized in the Communist Party) committed to using their power to that end
(Lenin, 1965: 349). Lenin thus deployed a complex analysis which related but also kept
distinct power and class processes. Very few of Lenin’s critics or followers followed him
in this kind of analysis. Instead, most collapsed power and class together, usually in analyses that focused mostly on power as if it subsumed class.
[...] The USSR after 1928 thus
defined itself as socialism and socialism as the opposite of capitalism.
Two related patterns of Cold War debates warrant attention. First, anti-Soviet literature referred mostly to ‘communism’ as what existed in the USSR, Eastern Europe,
China, Cuba and so forth. In contrast, pro-Soviet literature mostly saw ‘socialism’ as what
existed and communism as a future goal. Cold War debates thus often resembled dialogues of the deaf talking past one another. Secondly, serious disagreements among the
critics of capitalism entailed competing claims to the term ‘socialism’ and thus a proliferation of different meanings. For example, critics of both private capitalism and the
USSR’s socialism developed terms like ‘democratic socialist’ and ‘social democrat’ to
define the qualities and limits of state intervention (e.g. Sweden, Germany and France
after World War Two) that they preferred in their definitions of ‘socialism’. In this article, we use ‘state capitalism’ to refer only to societies where the state form of capitalism
prevails, where state officials appropriate most surpluses. We avoid use of the term socialism not only because of its multiple and clashing usages, but also because they all distract
attention from the organization of the surplus which is our focus in (as well as our definition of) class analysis.
And here's an interesting take on the terminology from a Chinese perspective:
two different stock phrases
that have been widely used to describe the Chinese economy of the Reform era: “state capitalism” 国家资本主义and “socialist market economy” 社会
主义市场经济.
What the term “state capitalism” suggests is that the Chinese economy
today evinces all the signs of a capitalist economy—dominated by capital,
profit-driven, and with wide income gaps between capitalists and their hired
workers—except that the state plays a very large role, most especially in the
form of interventions in the economy and state-owned and managed corporations. The difference from the planned era is that market forces and a profit
ethic have replaced planning and a revolutionary, redistributive ethic. What
the term highlights is the large role of the state and the essentially capitalist
nature of the system.
The other widely used term is “socialist market economy,” the official
Chinese formulation since about 1993. Here the idea is that the economy is
market-oriented and market-driven for growth, just as in capitalist economies, but it is for a socialist purpose. Now, “socialism” can be understood in
many different ways, including planning and state ownership, but in the context of this article, and in the Chongqing experiment, it is intended to mean
above all a mixed state and private economy that comes with social equity,
summed up by the expression “getting rich together” 共同致富. It means
development (“getting rich”), but development with equity, not without.
What has been happening in China in the Reform era approximates in reality “state capitalism” more than “socialist market economy.” That is part of
the reason there have been so much criticism and opposition from China’s
socially conscious, progressive intellectuals, who do not reject the market but
believe that the ideals of social justice from the revolution have largely been
given up for the ideals of individual pursuit of self-enrichment.
Acemoglu and Robinson probably have the broadest view of state capitalism:
To understand the logic of state capitalism, it is useful to recall some early examples—not the socialist command economies or modern societies seeking to combat market failures, but ancient civilizations. Indeed, it seems that, like farming or democracy, state capitalism has been independently invented many times in world history.
Consider the Greek Bronze Age, during which many powerful states, organized around a city housing the political elite, formed throughout the Mediterranean basin. These states had no money and essentially no markets. The state taxed agricultural output and controlled nearly all goods production. It monopolized trade, and, in the absence of money, moved all of the goods around by fiat. It supplied food and inputs to weavers and then took their output. In essence, the Greek Bronze Age societies had something that looked remarkably like state capitalism.
So did the Incas as they built their huge Andean empire in the century before the Spanish arrived. They, too, had no money (or writing); but the state conducted decennial censuses, built roughly 25,000 miles (40,000km) of roads, operated a system of runners to send messages and collect information, and recorded it all using knotted strings called quipus, most of which cannot be read today. All of this was part of their control of land and labour, based on centrally planned allocation of resources and coercion.
How is it that societies as disparate as the Greek Bronze Age cities of Knossos, Mycenae, or Pylos, the Inca Empire, Soviet Russia, South Korea, and now China all ended up with state capitalism?
The answer lies in recognizing that state capitalism is not about efficient allocation of economic resources, but about maximizing political control over society and the economy. If state managers can grab all productive resources and control access to them, this maximizes control—even if it sacrifices economic efficiency. [...]
inclusive institutions require a private sector powerful enough to counterbalance and check the state. Thus, state ownership tends naturally to remove one of the key pillars of an inclusive society. It should be no surprise that state capitalism is almost always associated with authoritarian regimes and extractive political institutions.
There's almost no discussion in the literature of whether Russia is socialist nowadays, but there's occasional discussion about China; in one such discussion the following criteria are drawn
There is no generally accepted definition of “socialism,” and there seems little
point in arguing over whether a complex reality coincides with a simple and arbitrarily defined label. Instead, the strategy of this piece is to advance four general
characteristics that are plausibly related to a broad range of conceptions of socialism:
that is, we will be talking about descriptive characteristics of socialism, rather than
“models.” Whether or not the reader accepts that these features are related to a
coherent ideal of “socialism,” raising the question of socialism in this way can help
to gain a fresh perspective on the current reality of the Chinese economy.
In this spirit, a plausibly socialist system would be judged on the following four
criteria: capacity, intention, redistribution, and responsiveness. First, a socialist
government controls a sufficient share of the economy’s resources that it has
the capacity to shape economic outcomes. One traditional definition of socialism
includes “public ownership of the means of production,” but “capacity” is here broadened to include the ability to control assets and income streams, through
taxation and regulatory authority. Second, a socialist government has the intention
of shaping the economy to get outcomes that are different from what a noninterventionist market would produce. Third, because a socialist government typically
justifies itself as benefitting those citizens who are less well off, it is natural to look
for evidence of whether such policies are succeeding in the outcomes involving
growth, social security, and pro-poor redistribution. Fourth, a socialist government
should have some mechanism through which the broader population can influence
the government’s economic and social policy, so that policy shows at least some
partial responsiveness to the changing preferences of the population.
So, while state control (and ownership) is considered a criterion in this paper, but it's only of four "socialism" criteria. And as an aside, with respect to China on some of these criteria:
Summing all four components, the Chinese government had direct or indirect
control of 38 percent of GDP in 2015. [...] The official position—written into China’s Constitution—
is that while multiple ownership systems coexist, state ownership is the “leading
force.”
[... However] China is certainly not a welfare state. China has virtually nothing in common
with countries like Cuba or Brazil—otherwise so different—which have made
substantial efforts to transfer money directly to the poor and to invest in social
services. In China, transfer payments of all kinds are low and are also restricted in
important ways. However, even in this respect, there are important differences with
the situation 20 years ago. In the mid-1990s, China was doing almost nothing to
redistribute income. [...] Today,
there are four different medical insurance and pension systems, which between
them cover virtually all Chinese citizens. However, the actual flow of resources
through these combined systems is still modest. The government’s direct contribution to social welfare benefits is still strikingly small. In 2014, budgetary outlays for
education by China’s government were 3.6 percent of GDP; for health, 1.6 percent
of GDP; and for public housing, 0.8 percent of GDP. These are all strikingly low by
comparative international standards.
While there's no such equivalent declaration (on the preeminence of state property) in the current Russian constitution (duh), a US Army War College study did find that Putin had expressed some doctrinal beliefs in the nationalization of their energy sector, or at least in the creation of some national champions. Interestingly, the same articles (of Putin) highlighted there also mentioned that this was expected to increase welfare for the average Russian (although whether by "trickle down" or outright redistribution is unclear form these snippets):
Putin professed his views on the subject of nationalizing strategic national
resources in a 1999 article “Mineral Natural Resources in the Strategy for Development
of the Russian Economy” by highlighting the need for the state to maintain high
regulatory control of the resource extraction industries. In what amounts to a blueprint
for his campaign to re-nationalize industry, Putin stated that a key role for the state to
play, particularly within the natural resource industries, is the “creation of large financial industrial groups – corporations with an interbranch profile that will be able to compete
with Western transnational corporations.” In this article, which was published before
his assumption of the Presidency, he also makes it clear that he views the government’s
support for industries involved in the extraction of strategic natural resources as the
means to “make Russia a great economic power with a high standard of living for the
majority of the population.” Additionally, he justifies a turn away from privatization by
stating that, “the experience of countries with a developed market economy gives us
many examples of effective state intervention in the long-term project to exploit natural
resources.”
Putin gave a more sinister preview of his philosophy on the role of government in
controlling strategic aspects of the economy in an article entitled “Russia at the Turn of
the Millennium” which he published December 30th, 1999, the day before he assumed
the role of acting President, replacing the ailing Boris Yeltsin. He stated, “Today’s
situation necessitates deeper state involvement in the social and economic processes. The state must be where and as needed; freedom must be where and as required.” In
almost unprecedented historical fashion, Putin published his manifestoes on the state
control of strategic industry and resources, and then actually rose to power to
implement them.
I guess these (ideological) articles of Putin were largely ignored by other writers on the topic of Russia nationalizations. Interestingly however, not even this War College study uses the word "socialism" anywhere.
As percentage of GDP Russia spends more on social programs than China... or at least it did 10 years ago, from when I could find (comprehensive enough) comparative data, but still was below OECD average. (From this point of view Russia is "more socialist" than China.)
From more recent data, Russian spending on welfare (as percentage of GDP) has somewhat increased since then, mainly due to a (relative) pension expenditure increase:
In 2015, total social spending in this country [Russia] accounted for 17.4% of GDP according to the cost structure, proposed by the OECD, or 20.3% of GDP when accounting for funding of all levels of education.
