The biggest change, militarily speaking, was in the size of militaries involved before the Wars of the French Revolution and after. To give you an example, the British army, on the eve of the American Revolution in 1775 was something like 48,000 soldiers over its entire empire. For a sense of comparison, Wellington had about 30,000 British soldiers (Not counting allied soldiers) just for the Battle of Waterloo in 1815. At the Battle of Leipzig in 1813, the French army alone suffered more casualties than soldiers existed in the British army only a few decades prior. The French concept was called the levee en masse

Basically, war on this scale was completely unprecedented in history, and the necessity of raising such large military forces required changes in the states that supported them. In Britain, you see more influence going to the House of Commons along with greater governmental centralization. Soldiers also had to be supplied, so you needed vastly increased industrial output to produce the weapons, ammunition, clothing, and so on that they all required.

All in all, I've always thought that the Napoleonic Wars did away with the last real vestiges of European feudalism, at least in Great Britain, and after 1815, we see something approaching what we could consider the modern centralized state.