I'm really looking forward to the day where the AI is solidly-better than me. Right now, I use the AI to control theatres that are not the centre of attention.
After the Vichy trigger has gone off, and I have occupied Britain, France and the Low Countries, I set all of it up under one BIG theatre, and then attach all the garrison units to it directly. I turn on the AI, click on the provinces that I want protected, and forget-about-it. The AI is EXCELLENT for dealing with partisans this way - they hunt the little buggers down much better than I could.
The Theatre AI still has MAJOR problems keeping command lines within distance, planning attacks optimally so that units stay together while still moving FORWARD, and properly exploiting break-throughs.
The AI has to learn how to think about preparation in terms of the command structure it is presented and how to move the entire formation toward the goals as expediently as possible. There is still WAY too much lateral movement along the front. The AI tends to want to send units hundreds of miles in order to exploit openings and weak spots. Of course, by the time the units get there, those openings and weak spots no longer exist, so the AI sends those same units hundreds of miles again looking for the next spot.
The AI has vastly improved at seeking flanks and expanding frontage. I have found that I have to watch very carefully where I attack or my first units into the province can get ganked!
I would like to see more work done with teaching the AI to utilize different formations more creatively - army corps and armys especially. Keep formations together, attack along consistant vectors to keep formations moving in the same direction, and limit lateral movement along the front to an absolute minimum!
The only thing that would make the AI even better is if it could actually evaluate my entire armed forces and suggest different combinations to achieve goals. Especially after Bitter Peace when invading India. Too little force gets bogged-down, to much starves on lack of supplies - I wish there was a supply calculator that allowed me to figure out a good balance for that. Even better: Let the AI do That!