they're all at least decent, none of them are complete crap.
i'd say rome is the least flexible; if you don't get early iron, you've pretty much handicapped yourself because they're not too good at doing the whole peaceful building thing, scientific, religious etc. if you do get iron though, and combine it with catapults, then you can flatten 1 or 2 opponents and you're in the driving seat. or 3/4/5/6/7 if you're going for conquest/domination
babylon becomes ridiculous if you can navigate their crap expansion at the start and avoid early wars. yeah, they've got the bowman, so you can war decently, but that slows down your already crap expansion. once you've got the cities, roads and the buildings down, they just run away with the game, scientifically and culturally (and by extension, commercially and millitarily). once you get settled down with the minimum avoid of troops to avoid being harassed, you can just build and research better than anyone else.
greece is basically perfectly suited for building and science and all that. plus, with the hopilite, nothing will bother you until knights, by which time you're already running away with it. i'd say they're worse at wars than rome but better than babylon. also, lack of cities isn't a big problem for greece, unlike most non-agricultural civs, because the cities you do have with be worth 2 or 3 of the AIs.
egypt is a bit weird. they can do early wars decently if you're on a lot of flat ground, but if you're not then you're stuck. they're not great for researching so if you don't or can't go for early war then you're stuck between two or three different options and not really doing anything that well. their traits don't really have much in common, they don't really compliment each other. basically, they're decent, but they don't excel at anything really.
persia is basically the best of rome + the best of greece. if you want to play all peaceful and build stuff, then they can keep up with anyone. and if you want to just steamroller everyone then they'll do that just fine as well as long as you have iron. i'd say they're the best out of these 5.
i'd rank them:
1. persia
2. greece
3. babylon
4. egypt
5. rome