From: east coast, usa
Unless its an emergency, I often wait a day to let someone else answer, I don't want to be a post hog.
There is no Artificial Intelligence, as Josh said there is a Programmed Opponent. This means that each scenario is designer specific. The designer implements a PO as he sees fit, there are no requirements. Some have a PO, some do not, some have a PO for one side, some for both.
If there is a PO in a scenario, how good it is varies. I'm a TOAW solitaire player for 10 years so I can say that the only way to find out is to play a scenario and see how it goes. The list of scenarios is huge, but from my limited experience pretty good solitaire play can be had with these:
In the Classic Folder:
Desert Storm 91 (if you like rolling over everything)
Kursk 43 (if you like beating your head against a wall)
WWII East Front
Soviet Union 1941
WWII West Front
Autumn Fog 1944
Operation Varsity 1945
It took 19 minutes for this answer.