Umm, I haven't played Civilization but I think I know something SERIOUSLY wrong with it.
You start from, well years back, right? BC ages, if so, then you change the future with the actions then, thus making the events that happen (like 9/11 or Hundred Years War, or anything really), making it a completely unrealistic game, that's what I read, and I came up with that, please don't flame me, just tell me if I'm wrong with the events happening
As far as I knew things like 9/11 and world events do not even occur in Civilizations. I may not be paying attention or something, but I did not know that world events existed and could be activated. Your importation of goods and how much you help allies in wars affects how much they like or dislike you in future, and your selected paths on the technology tree change what technologies you can unlock in future - but as far as I know, that's the extent of changes in the future.
I have to side with Civilization. I've played both, and both are good. But Age of Empires has short games that aren't very challenging(for me anyways) and Civ. games take time and thought along with patience.