The AI doesn't really change according to your difficulty. It always just alters the level of cheating. Basically, it goes from "man, when will the enemy ever attack me" to "why the bloody shit does the enemy ALWAYS have 9 full stacks of units EVERYWHERE?!" It's good fun though, seeing 100 horsemen survive wave after wave of impossible odds. Patting yourself on the back for every victory, because they were insane.
But fighting the Mongols and Timurids on the hardest difficulty setting is crazy. You'll know what I mean if you've actually done it. Want to know what LITERALLY 10,000 arrows fired from 10,000 triple gold chevron horse archers look like? Fight Mongols on hardest difficulty. So fricking unfair. They bloody bring rockets and heavy mail when you barely even have trebuchet technology. I remember them spawning (during the mongol invasion event) with 20 stacks moving as one unit, each with perfect stat generals. Still fun though, if your computer can handle that many troops on screen.
There are a lot of mods that claim to improve the AI's intelligence, but I've never really seen anything too impressive. What I just do is pretend those were medieval strategists doing their thing (which makes sense), where most of the people of the time were meagre in the intelligence department, but once in awhile you come across a really strong foe.
It's worth noting though, that in my time playing it online, actual players are generally stupider than the AI... so... Yeah, take of it what you will.