In the first game, there is no difference between the Atlanteans and Greeks in terms of tech/units or buildings (aside from a very durable type of wall). While this could be chalked up to Gameplay and Story Segregation, there is this little line of dialogue spoken in the very first mission by Theocrat - ...he already complains that we do not pay enough attention to the Greek colonies..
Even more of a case of fridge brilliance once you realise that Atlantis was once thought to have inspired the civilizations from mesoamerica to Egypt and Greece!
Atlantis was already something of a Mary Suetopia in Plato's tales, it fits for it to be overpowered in a game explicitly based not on historical fact, but on myth and legend.
Atlanteans gain Favor based on how many Town Centers they control. While this is just another element of the Atlanteans that is simplified to make that civilization a Skill Gate Character, it also makes sense. The Atlantean tech tree worships the Titans, whose goal is to break free of Tartarus by means of Gods Need Prayer Badly. By capturing more Town Centers the player directly expands the influence of the Titans into new real estate, for which they are rewarded.
A mission in the expansion involving an Atlantean assault on Mount Olympus allows the player to transform his human reinforcements into myth units against their will.
Further to this: one of the god powers you can get in this mission is the Curse power, which is used to turm human soldiers into pigs. Just like normal pigs, these become yours if you have more units around them... which means you can take these pigs and turn them into myth units. Pigs that once were your enemies now are monsters loyal to you... and you can harvest food from them...