Can't believe that this thread is still going... Both Korea and Babylon are awfully similar in pretty much everything. The bonuses are slightly different but they achieve the same goal, just in different timings that the player has to adjust to, that's all. Also, I've a lot of people here talk about how Babylon is a 1 trick pony while Korea is versatile, that's simply false. Babylon is as versatile as Korea because every civ, no matter the victory condition, fills all their great scientist slots and usually nothing else unless you got huge cities that you simply ran out of room. So in that case Korea and Babylon are pretty similar, as you won't be filling every single specialist slot as Korea, only scientists and perhaps artists if going for a culture victory. Also, because science is the focal point of every match, no matter the victory condition, great scientists, especially early on, are more important than any other great person, though later great artists become equally if not more important if pursuing a culture victory. So in that sense, again, Babylon's UA evens out with Korea, which leaves both civilizations as very versatile thanks to their massive science lead over everyone else, and with said science lead the flexibility to do whatever you want with it.
In case I wasn't clear, I was referring to high difficulty games, so Immortal+Deity, perhaps Emperor too. In lower difficulties it simply doesn't matter as much since the AI is too weak to be of any real concern. So basically, the main difference between Korea and Babylon is not in their flexibility but only in play style. As Babylon you generally want to rush writing ASAP, only getting the luxury techs you can work immediately(or settled on), and you can also afford to significantly delay construction since your Bowmen are almost as good as CBs. As Korea on the other hand rushing Writing is not as big a deal so you can get a few more luxury techs early or rush construction if needed. Also as Korea you can decide to not use CBs at all but instead use Catapults and turn them into H'wachas ASAP for beastly defensive units that can switch to the offensive in a pinch. The disadvantage is obvious, you generally don't want to rush Physics so it's far from an optimal tech path. On the other hand it gives you a much stronger army for later, since H'wachas upgrade into the siege line while CBs upgrade into the archery line, losing range at Gatling Guns and eventually merging into Mechanized Infantry at the very end. So those early H'wachas, if you manage to not get them killed, will eventually become the almighty Artillery and Rocket Artillery, which is by far the best ground unit in the game, basically Longbowmen on steroids.
So again, just potential differences in play style. Neither Korea nor Babylon has a clear upper hand against the other.