AI is doing well compared to other similar games. Its not perfect but certainly up to standard.
It plays quit well strategically, can handle diplomacy fairly. However it sometimes tend to start more wars than it can handle. I saw AI fighting two opponents while declaring war on another in clearly hopples situation.
It does not handle trade too well and gets subsidized with extra money from game (even on normal difficulty) to be able to handle its economy ...well, if you can call it like that since up to my experience it simply keep labor deployment at preset levels without regard of region strong and weak points (I suspect AI gets subsidized by resources as well or is favored when building units in some other way) and builds development here and there. This is enough to allow it to build and maintain army big enough to be of challenge to player. It however tends to break if you play scenario longer than intended since AI sometimes end up with huge armies it clearly would have no chance to sustain if subjected to same economic rules as player. While whole (detailed) economy system is well modeled, it seems it was build for player not for AI :)
As for detailed naval combat I do not have too much experience, but AI have some serious problems managing and deploying its fleets it seems. It tends to build ships but strangely it doesn't fill its fleets with them. For example if English fleets gets teared in the process of war it retires them for the rest of the game while at the same time building and maintaining dozens ships through its provinces ...without attempt to reform scattered fleets and sending them to sea. You can sail strait for England and invade it if you want without English AI doing something with all its idle ships to oppose you. I also did not noticed AI to ever build new fleet.
As for detailed land battles, AI can fight but doesn't expect miracles from it. It seems to deploy its units piecemeal, attacking you individually without its units giving support to each other. I newer saw AI deploying in to some kind of formation. Sometimes I see enemy units idle, facing one direction while been pounded from flank or rear. For what ever reason such units stays still (maybe resting?) it doesn't seems to be smart enough at last to turn to face your fire. Another thing you can notice is that it always withdraw its disorganized cavalry units to rest and reform to one corner ...always the same one and without regards to own or yours positions. Player can easily exploit it by sending unit or two there and make sure those cavalry newer reforms and fight you again.
This sad, AI can beat you good if it have superior numbers or superior morale but with some experience you can expect always to beat it on at last bit equal terms.
All this written, this game AI is in better standard of contemporary strategic and tactical games (AI of Gary Grigsbys games is pitiful for example ...to such extend that I would not call it Intelligence at all, just AS - Artificial Scripts) but if you want AI which can present you some challenge you have to play electronic chess :)