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Both are excellent and both will eat your free time like a black hole eats, well time and everything else.

The primary difference is Age of Empires is a RTS, real time strategy. That means everything happens in real time, how quickly you expand, where your units move, etc all depend on how fast you can click and move your mouse. Against the computer for Age of Empires not a big deal, but with harder versions of that kind of game it can be an issue (at least it is for me, I'm no mouse slouch but I just don't like the hyperactivity required).

Civilization is a turn based strategy, so everything is based on turns, units have movement points and can only move so far per turn, etc etc.

I prefer this because you can take your time to plan a strategy if you want.

I highly enjoyed both of them, you can't go wrong with either one.