While Germany is a federation of states, France has chosen to devolve some of the power to its regional governments. How has this affected the development of these countries? Has one system fared better than the other?
The two states of affair are a result of history, so I'm not sure your question can be answered as is.
On the French side, the historical process has been to centralize ever more power in Paris. Initially it was about growing the royal domain and keeping French vassals in check. Power concentration in Paris continued for all practical intents and purposes all the way to 1982. Put another way, all French roads have been leading to Paris until recently, and it's not that big a stretch to suggest that decisions to develop areas outside of Ile-de-France were being taken in Paris.
On the German side, in contrast, the Holy Roman Empire was a hodgepodge of semi-independent states operating under an elected emperor that had little practical authority on its subjects' realms. Besides the rise of Prussia, two key events that led to modern Germany are Napoleon I dismantling the HRE and reorganizing it as a confederation with a much smaller number of larger states, and Bismarck managing to unite the latter states against Napoleon III who he tricked into attacking Germany. Put another way, the future Federal states of Germany have historically enjoyed a very large degree of autonomy throughout their history. It should be no surprise, then, that Germany has no city that concentrates the bulk of its economic activity and economic decision making.
Which of the two is hard to say. But I'd surmise there's little correlation between how the country's administration is organized and how its industry fares. There are many other important factors that kick in, such as the presence of transport networks (rivers, roads, rail) or that of raw materials, education and work ethics of the workforce, capital availability, the presence of business clusters, and so forth. Intuitively, each of these are a whole lot more important.
Superficially you could put forward that a lot of economic activity self-organizes across Germany, whereas it takes an impulse from Paris to try to create, say, a tech cluster in a region like Bretagne. But economic activity in Germany actually is concentrated in a few areas, and it is in these places only that things self-organize. Berlin is to Brandenburg, in this sense, what Paris is to France. Or put another way, the dynamics of centralization vs decentralization and its impact on the economy merely exists, I think, at a different level in Germany than it does in France.
How has this affected the development of these countries? Has one system fared better than the other?
This is reflected in a variety of ways. Each has areas where they excel although one would be hard pressed to find a consensus over which was better overall, and there has been convergence of the systems, especially in the post-WWII era.
Historically, the industrial revolution in France was led more heavily by the state and big business than in Germany where private firms and small businesses played a larger role, although both countries had a more state led industrialization path than England.
In Germany, a lot of local infrastructure development (e.g. opera houses) was developed on a competitive basis with different states seeing each other as rivals, while French infrastructure development has tended to involve more "master planning."
The French health care system is run by a national bureaucracy. The German health care system, like Obamacare, involves a mandatory health insurance system where health care is administered primarily by private insurance companies. Both have their virtues, but they reflect different levels of comfort with centralization.
As another example, the German university system was heavily tilted towards STEM programs for private industry, In contrast, the most prestigious university in France is the Ecole national d'administration which trains senior civil servants.
Political scientists often speak of the French Civil Service as a separate branch of government from the politically appointed executive branch officials of the French Presidency and Prime Minister's office. The French Council of State (which runs the administrative law system and sets top level regulatory policies) is widely viewed as the best run administrative law system in the world. It is also from France that we get the word "Bureaucracy" before their centralization developed modern style bureaucracy earlier than any other country in the world.
But, it was also not politically responsive to have to contact the French equivalent of your Congressman if your neighborhood street light goes out. French governmental provision of services has tended towards the technocratic, while German governmental provision of services has been more political.
Public Sector Unions
The differences between the centralization of the systems has also likely contributed to the pattern of public union action.
France has a long history of national, public sector union strikes that are effective because the centralization of the system makes the entire nation a natural bargaining unit for them.
In contrast, in any federal system, including Germany's, the fact that one state's public sector workers are engaged in labor action does not affect other states. In much the same way, as this answer is written, all of the teachers in West Virginia have been on strike for several days shutting down all public schools in that state, but other U.S. states have barely noticed.
Different Kinds Of Federalism
Federal systems, however, differ a great deal from each other. Germany and Canada, for example, centralize more kinds of legislation (while still decentralizing administration of those laws) than the United States, which in turn, centralizes more kinds of legislation than Switzerland.
As a result, federal states like Germany, with a high level of centralized legislation have not had the same regulatory race to the bottom that has characterized federal countries like the United States, where legislative authority is more decentralized.