The AI in Civ3 cheats exactly as much as the AI in Civ2 does (plus more, because the AIs freely exchange their techs at low cost with each other, while charging you an arm and 2 legs).
What engine in Civ3? The graphics engine? Fah! Graphics do not make a game. In fact, graphics are the _least_ important factor of a game. Crisp units = irrelevant.
The political model of Civ3 is much weaker than in a fairly large number of games, actually. It is certainly not unparalleled. And a decent political model means little with rampantly cheating AI.
The difficulty level of the AI in SE4 does _not_ cause them to cheat. The bonus does, but the difficulty level does not. This is the crucial difference between SE4 AI and Civ AI: SE4's AI can be played on high difficulty levels without any bonuses given to it. In Civ, you have to suffer with rampant AI bonuses at higher difficulty levels.
But the AI cheating doesn't really matter. Civ and Civ2 were still very fun games with their rampant AI cheating. Civ3 is just a poorly designed game overall, and has many inescapable flaws (which I don't care to enumerate again at the moment), in addition to miserably failing to carry on the Civ legacy. Instead of building upon Civ2, it destroyed nearly all of the improvements that had been made in the Civ2 series (esp. the expansions). And then they have the gall to release the game in a rather early beta stage, and charge us for the rest of the game later on!
Civ3 represents the first Civ game that is all about flash over content. I certainly hope that if a Civ4 is ever made, it takes nothing from the abomination that is Civ3.
And overall, you haven't really given any reasons as to why Civ3 is a good game.

Anything other than crisp graphics or political structure?
[ April 23, 2003, 09:00: Message edited by: Imperator Fyron ]