Some similarities and differences in a French context (relevant because a large portion of the electorate there votes for the extremes of the [conventional] spectrum) are detailed by Mayer (2011). To pick some examples, in the 2007 election
On a global indicator taking into
account the occupation of the interviewee and of his or her parents, some 70
percent of Le Pen and Besancenot voters had at least one link with the blue-collar world (as against 56 percent in the total sample). Seventy percent found
it hard to get by on their present income. If one combines this economic stress with the fact of being unemployed or having a fixed-term contract, one gets an indicator of social precariousness, a condition that affects 15
percent of the 2007 French Panel sample, but one Lepenist voter out of five
and one Besancenot voter out of four.
Yet if one looks more closely, differences do appear. Among Le Pen voters
there are more blue-collars belonging to the manual working class. One finds
more of the lower service class, the “post-industrial” proletariat, among Besancenot supporters, a trend noted by Nathan Sperber in a detailed study of
extreme-left voting in 2002. Lepenist voters are older, the majority of them
over 40, and one quarter are retirees. The majority of Besancenot voters are
under 40, and only some 10 percent have retired. Being younger, they are also
more educated. Over 40 percent have at least the baccalaureate, the degree
that marks the end of high school in France, double the proportion found in
the Le Pen group; and 10 percent of Besancenot supporters were university students at the time of the survey (as against some 2 percent of Le Pen voters).
Lastly, the Besancenot group is more multicultural, 30 percent of them have a
foreign parent or grandparent, twice as many as among Le Pen supporters.
Leaving demographics and moving on to platforms:
The fact that the extreme Right and the extreme Left both are particularly hostile to European integration is one of the arguments often used to emphasize
their convergence, as suggested by the provocative title of Dominique Reynié’s
book Le Vertige social-nationaliste: La gauche du Non et le référendum de 2005.
Indeed, when asked how they voted in the referendum of 2005 on the European Constitution (Figure 4), respondents intending to vote for Le Pen or
Besancenot in 2007 both declared an exceptionally high level of “No” votes.
As Sylvain Brouard and
Vincent Tiberj have shown, left-wing voters in general defend the public service and the welfare system against a European Union (EU) they associate with
big business and economic neo-liberalism; there is a social dimension to their
opposition, while Le Pen voters associate the EU with open borders and massive flows of immigration threatening French national identity.
One finds the same kind of contrast in 2007. When presented with a list
of problems and asked to select the two that would be most important for
them at the time of voting, Besancenot supporters put forward social issues.
Unemployment, social inequalities, and purchasing power were ranked first or
second by respectively 38, 35, and 27 percent of them. The hierarchy was different for Le Pen voters; they gave priority to the issue of immigration, followed by unemployment and crime, chosen by respectively 49, 34, and 25
percent. A majority of both groups believed that their candidate offered the
best solutions on the issues that mattered most to them. If one compares the
choices of extreme-right and extreme-left voters to those of the sample at
large, computing for each issue the difference between the average answers
and those of Besancenot and Le Pen voters (Figure 5), the former stand apart
by the importance they attach to social inequalities and taxes, the latter by the
importance they give to immigration and crime. And both groups appear
almost systematically opposed on ten out of the thirteen issues. When one
rates an issue higher than the sample average, the other will rate it lower.
They clearly have antagonistic visions of the world.
So the modern extremes may meet on some issues, but not on as many as one might think. And based on these issues a score of "ethnocentric authoritarianism" is computed, which (unsurprisingly) oppositely varies with the propensity to vote for the extreme left or extreme right candidate(s):
So while it's easy to find similarities based on past authoritarian regimes (nazism vs stalinism etc.) in terms of methods (physical suppression of opposition, personality cults etc.) a look at the more democratically inclined extremes of today finds the difference in terms of platforms/ideology with relative ease.
Furthermore, not only does the extreme left does not look like the extreme right in terms of values/ideas, but there's also more ideatic variation at each extreme than in the center, in Europe at least. According to Hanel, Zarzeczna, and Haddock:
There is a popular belief that individuals within political left- and right-wing
extremist groups share very similar values and attitudes in contrast to more moderate
activists, who are seen as more heterogeneous. Likewise, some even argue that all
extremists, across the political left and right, in fact, support similar policies, in a view known
as ‘Horseshoe theory’ (see Choat, 2017). However, not only do recent studies fail to support
such beliefs, they also contradict them. For example, van Hiel (2012) analyzed variability in
values and anti-immigration attitudes among political party activists who reported affiliation
with left-, right-wing, and moderate groups. Analyzing European Social Survey data (2002-
2008) collected from Western European political activists, van Hiel found a substantial
amount of heterogeneity of values within left- and right-wing party members, and greater
homogeneity reported among members with moderate views. However, he did not directly
compare the variability across groups of individuals that identified themselves with the
political left, right or center.
[Thus, in the new study...] Specifically, we tested whether the
values of left- and right-wingers are more diverse than the values of those in the center across
all European countries, using a series of Levene-tests for variance homogeneity. The results
showed that left-wingers were significantly more heterogeneous than those in the center for
all ten values supporting the view that extreme left-wingers form a less
homogeneous mass. Also, right-wingers were significantly more heterogeneous than those in
the center for all values except for conformity.
[...] Overall, a
higher proportion of variance in value endorsement was explained by country membership
among more extreme political supporters compared to individuals with moderate views.
So there's perhaps a country-specific flavor to extremism, but the moderates tend to look the same across countries. (An interesting form of globalization, if you ask me.)
Van Hiel also offers an interesting perspective as to why the Horseshoe theory may have come about, namely the relative uniformity of the moderates:
Imagine two extremists: would you consider them to be more alike to each
other than two moderates would be?You probably do. It seems to be common
knowledge that members of extremist groups are ‘all alike’, and this idea also
seems to pervade the literature, although it is difficult to provide citations that
explicitly convey this message.There are, however, social psychological explanations
for why extremist groups are often considered to be composed of
homogeneous members. For example, almost by definition most people are
moderates, and there is only a small number of extremists, which places them
in an outgroup position. Social categorisation theory asserts that outgroups
tend to be perceived not only as different from the ingroup, but also as more
homogeneous (the outgroup homogeneity effect), which may explain why
members of extremist groups are perceived as being very similar to one
another (e.g., Vonk & van Knippenberg 1995).