The AI in Total War isn't really improved from easy to expert level, what they did was increase the "morale" values of the enemy AI, thus they don't rout as easily and they "decreased" the "morale" your your units, thus it seems the AI is playing a better game. There are also other modifiers that they increased for the AI and decreased for the player, makes it seem like the AI is "tougher", but, it's really not in the sense of AI, just in power. Peasants can be a challenge to a human player on the Expert setting.
I play Total War on Expert and still wipe the AI even outnumbered 2-1, mainly because the computer AI never protects it's leader/general during the battles, and if it's defending it's so easy to lure it out of it's tactical advantage of forest/trees or high ridge with a calvary unit, mounted crossbow or mounted archers work rather well for this. A heavy calvary/knight unit and one mounted missle unit seems to always do the trick for eliminating or routing the general/leader of the computer AI, even on the expert setting. But, I found a very good mod The Patrician v1.2, it's a roman era mod for MTW and every AI is set to aggressive/expansionist, while the AI is not any better, I often find myself fighting more than I have units to fight with in this mod vs the vanilla version of MTW. All leaders/generals start out as a +7 to +9 leader also. Your offspring can make you or break you in this game.
Now for CMBB and CMBO AI, yup, it's not a great attacking AI, but, you can improve it's chances against you if you will up the amount of men/armor/support it gets by 25% and giving it HIGH level units and +3 advantage. This is the way I play against the computer AI when I want it to be the attacker. Also only give yourself MEDIUM or GREEN units and you will find yourself in a much more challenging game vs the attacking AI. But, on the other hand the AI is pretty strong on the defense, especially if you give it these same settings. None of these settings improves it's tactical movements, but, just the sheer extra numbers and quality of weapons and units makes for a more challenging game.
For games like these and the AI, I would like to see them give it a "Dirty Tricks" file, and randomly from time to time the AI would use these "scripts" on tactics to use against a human opponent. It would need many so there was enough randomness the human couldn't really figure out which one the AI was using right off the bat. Some like stacking all your units to one side of the map and just rolling up the flanks of the human opponent, who's got his men/units spread all over the map. LOL I bet there would be screams of agony if that happened to a human player. Another would be to split it's forces in half, and put one on each side of the map and pincer the human player out of existance! heh, these are just some I have used against the computer AI, poor thing never had a chance! lol