I don't think the lack of resources has to do with a crappy AI, it's the developers who don't take the time "to flesh it out". Didn't Sony create the "Emotion Engine" for the purpose of an advanced AI*? And if that was so, it really hasn't changed the experience of playing against computer opponents much.
I think the AI problem is mostly due to the developers who really don't wan to take the time to make it as intricate and realistic as possible. Don't get me wrong, many developers do take the time to make good AI opponents, but when you look at games that are cash-ins on licenses, or just didn't have a lot of development time, they have pretty weak AI opponents.
But there's one thing that bugs me more than a weak AI opponent, and that's the AI who is a friggin cheating bastard. Like the opponents in Need For Speed Underground who run you off the road or how every CPU controlled car in Test Drive
practically tosses cars right in front of you to slow you down. It's one thing to have a weak AI, it's another to have what I call an "A-Hole AI", which almost ruins the fun of a game with frustration.
So, I don't think more resources in the hardware could make an improvement in a game's AI, it's really up to the developer and how much work they put into the code.
*If I'm wrong on the Emotion Engine thing, can someone tell me what it WAS originally for? I think it was nothing more than "blast processing", because I haven't seen the Emotion Engine in work since I've had the PS2.