Every game was good in its own way. Age III was great for LAN parties, because of its speed and scale; I think they managed to do a great job in terms of balancing, as well as making the game easy to play, but tough to master. (Although, the first expansion allowed for stupid-fast rushes with the Aztecs and Iroquois.)
Although I still enjoy Age of Empires II, with its expansion, my heart will always be with Age of Mythology. That was my first game I truly played competitively, and I felt they did an excellent job with the gameplay dynamics, and having the different civilizations actually be different.
Age of Empires Online was fun, for a bit. It had a similar type of pace and gameplay to Age of Mythology, but it felt pretty bland. They really botched the delivery, too. I did not mind that they released the game with only two civilizations, for starters, but not having a skirmish mode out of the gate was nigh-unforgivable. Their strategy for creating time-sinks was really poor, and the weapons/equipment feature was really kind of silly. In short, they had the basics down well-enough, but dropped the ball for sustainability and longevity. Why would I play a silly play-to-win AOE game that still lacked civilizations and features, when I can go play AOEII and enjoy everything?