I don't think the tech speed on the Babylonians is the issue right now. One issue is when the AI Persians spawn they often don't attack Babylon, and their units will just stand around and not pillage. This is sometimes expected from AI, but Persia should definitely destroy or severely affect Babylon. The Greeks and the Romans will also often not be able to take Babylon either. By the time the Roman conqueror event is over, the Babylonians will have been around longer than any other civ in the region, and just being established will make them a powerhouse until the Arab spawn.
For the human player, Babylonia is an easy game. It's about getting the right tech path, and then just surviving, since none of the civs in the area pose a serious threat before the UHV is done. I wouldn't say its a particularly easy survival game after the UHV though. I played one where I brought Babylonia into modern times, I would say the tech was about right, and it was difficult to keep stability up.