Civ III is good for when you want to sit down and play a game over days/weeks (depending on how much time you spend gaming). AoE II is good for those shorter moments - an average AoE II game against AI opponents for me can last about 1-2 hours.
Each is fun in their own way, and comparing a RTS to turn based is like comparing apples and oranges...
If I had to choose, it probably would be Civ III, though there is a lot of indecision in that choice. The simple reason being is that Civ III is more 'open ended' with game play, and there aren't any sort of "set in stone" rushing strategies used that dominate gameplay like in AoE and many other RTS games (IMO).