Turks in late period and Byzantines all periods.
A large part of the game is IMHO thinked to let the player live the fall of Constantinople and all the historical transition to the new Ottoman culture. That's the reason why playing Glory Achievements, the Turks are given a huge score with the conquest of Byzantium and that's why Turks have a completely new unit roster as late period approaches while Byzs must resist with the same units for all the game.