I like the different types of attacking/defending idea, although that's more to do with unit commands than an AI request, albiet with all new features, we HOPE Firaxis doesn't pull an SMAC and make sure the AI can use them too.
That said, I think the 'flavour' AI is probably best built by the modding community, who probably has the time and the resources available to really dig into unique behaviors and the like and constantly update their mods to adapt to human adaptations.
What I'd like to see from Firaxis' end is less to do with flavor AIs but just a more competent AI that makes for more interesting games. I don't completely agree with the idea that if the AI plays the same way, it gets old. Civ 3's AI like all TBS AI gets old because there's a lot of things it doesn't do well at all. After all the patches, the AI still doesn't understand how to use its 3 movement units. They storm into your territory, attack, and gets stuck out in the open waiting to be wiped out, whereas a human opponent would look for a thin spot in the border, use bombard units to soften the target, attack with their high movement units and make sure they have enough movement left to retreat into a city with barracks to heal and if that's not possible, the human players would build their own city for that purpose or bring lots of defensive units and stack their attackers behind it.
An AI that can do that would be hard to counter in the exploitative sense, the best a human player can do is adapt and build up sufficient defenses and combination of units to survive the attack, which of course implies costs, strategy, gambits and shrewness.
Imagine the couter system goes into Civ 4 (ie: pikes counter cavalry etc.). In order to properly defend their empire, players would need to figure out the shape of their opponent(s)' armies and build a defense to that and the AI is going to be doing the same thing. If the player has lots of Cavalry, they will build lots of pikes too. There may be more espionage involved and the like, but the adaptation that comes out of this is always lively and interesting. I have no doubt players will eventually develop rule of thumbs and 'catch all' defensive mixes that will do a job well, but the really good and dedicated players would want to go the extra mile and configure their defenses to more effectively counter the AI in THEIR GAME.
The AI of that order, which can build different unit combinations and which is going to hit you with combined arms when you go to war is going to be effective no matter how many games you play, you just have to pray your defenses and your intelligence on their unit type is good enough to stand up against their attack.
The most recent example of good AI coding that has altered the game is played is the upgrade of airpower in C3C with lethal bombard. The area where this has had the most effect is naval invasions. It takes much more planning to get it to work post C3C and I can still incur heavy losses of my escort fleet both from the improve AI warship rountines and lethal airbombard. There's no costless workaround or adaptation to that other than building lots of AA and having an airforce of your own, which is precisely the point the game should be moving players.
Adaptation with a price, rather than the exploitative sort of adaptation like the Artillery SoD, which to me seems to be the prescribed panacea to get out of every military disadvantage.