The main problem I see is that large empires are ALWAYS better than small ones. I finished two games (one on prince difficulty, one on king) each took me ~30 hours, and in the first I focused on diplomatic victory and the second on cultural victory and my empire didn't exceed 6 cities in either game, but each city had 25+ population at the end, while the only AIs' capitals were at ~10-15 population and their other cities were more like 5-10 population!
None of the AIs even considered another type of victory than domination (or those that did were quickly conquered), and so by the end of both games I had about 5 enemies left (down from 15), who each conquered at least half of their respective continent with total ease, while having enough gold and science to keep up with - and occasionally surpass - me AND have armies that could have easily wiped me out had they been smart enough to use them.
Also, even with a ton of wonders, because obviously my cities far surpassed theirs in terms of productivity, that gave me all kinds of bonuses, I was always just at the happiness barrier, barely maintaining my growth rate, even though I managed to trade for ALL available resources (15*5 happiness), had all the policies that gave me an advantage (-20% unhappiness from tile working population, -50% from unhappiness from number of cities, -33% unhappiness from tile working population in the capital)!
The only way I won was by using the grossly overpowered city-states for growth and culture and focusing on getting great merchants to get enough gold to maintain my relations with the numerous city-states!
What it comes down to is this: A cheating AI is no fun to play against, because either you quickly fall behind and are frustrated that the AI only wins by cheating, or you can keep up, then the cheats are too weak to compensate for the AI's lack of everything else and you are frustrated that you only win because the AI is too stupid to use its units! It's no fun defending against a superior army just to win because you built a citadel in that one bottleneck you deemed strategically important! Or because the AI attacks a city but does not know how to effectively protect its siege units! Or because you are on a different continent and the AI cannot grasp the concept of protecting their transport ships!
I had hoped Firaxis would finally allocate some development time for a really good AI that can outsmart the player without having to blatantly cheat to keep it from stumbling over its own feet, but apparently dumbing down the Civilization franchise for the masses and updating the graphics to look really shiny took up all the time ...