I want to throw myself into the whole split thing. Let's start with my favourite ancient civilisation: Babylon.
Before starting I'd just like to point out that I know like
nothing of any worth about Babylon, so I can only comment on the mechanical side here. But either way, here goes nothing.
The Kingdom of Babylon
Hammurabi
I have to agree with Sulomon here that in most games except maybe quick speed, and even then if you can conquer quick enough, the first part of Hammurabi's UA is very, very powerful. Especially when coupled with all the extra buffs towards social policies from the UA, UB *and* UU. That said, I like the overall idea and it really does a good job of symoblising something that is pretty tough to represent using the ingame mechanics, ie, good lawmaking. The only other thing I can say to criticise it is that it could be really frustrating attempting to make use of the UU's secondary effect given how irritating and fast trade routes are, we all know how annoying it is attempting to patrol your trade routes even with a pretty quick unit! It does work well with the UA though; a really cyclical civ.
The Kingdom of Babylon
Nebuchadnezzar I
In contrast I'd say Nebuchadnezzar I is slightly underpowered, but that might just be my playstyle. Its not a huge bonus being able to found your religion upon capturing an enemy captial, but I usually get a religion up early and only conquer in the mid-late game so thats maybe just me. Other than that, its a really great design, particularly the second half of the UA. Cyclical as all hell too.
The Kingdom of Babylon
Nabonassar I
Nabonassar I think seems like the weakest of the five, though its still not bad. I don't think the second half of the UA is useful at all, since generally losing a war so badly you have to give up cities is something people tend to avoid. That said the extra GS generation is so powerful I'd probably end up just making a load of crappy cities, declaring war on an AI and then giving them all those cities. So either way I don't think it makes for a good playstyle. The Chaldean too is strange, I don't understand what 'build a star catalogue' is; is it a building? In which case you have 4 uniques, and either way why wouldn't you just build an academy, unless the building yields more than 8 science, in which case it becomes OP. Is it a science boost? In which case, isn't it just the regular science boost? Or is it a UI, in which case, why not built an academy? I dun gettit. Aaand the UB is really really weak at the start of the game and absurdly overpowered at the end; very unbabylonish.
The Kingdom of Babylon
Merodach-Baladan
While I'm being a dick, I also don't really care too much for Merodach-Baladan. Nearly all of the bonuses are set up so that they only have any real effect after having pretty much lost the game, so unlike every other civ in the series, it receives no actual boost towards a victory condition save a potential +30% combat boost if you've lost and recaptured 6 cities, at which point you'd be so far behind that victory becomes impossible. I like the Sealander though, I'm surprised a river bonus didn't come up more often but the sealander makes perfect use of it. Furthermore, how would the UA actually work ingame? It would result in a lot of the player just sitting around doing nothing waiting for units to spawn and I dun think many players would have the patience for that and just ragequit after being eliminated.
The Kingdom of Babylon
Nebuchadnezzar II
Back to being nice, I really like Nebuchadnezzar II. I would say that the UA is odd for Babylon in that it works better the later the game gets, but mechanically its very interesting, especially paired with the unique siege unit. Maybe a teeny little bonus could be put on the end to keep her relevant in the early game? I feel like it really represents a sort of plunder and conquest society incredibly well, exporting bonuses from the peripheral cities you've conquered back to a lavish and fancy heartland. The catapult UU is really great even if it steps a teeny tiny bit on Assyrias big hairy toes, but ah well. The UB is a little odd though, its a cool effect but given how the UA and UU work, it essentially just equates to a huge food buff in the capital and nothing else. I'd probably also stick the effects of the original walls of Babylon on there, if perhaps a little toned down to compensate for the new bonus food buff. Either way, great ideas there.
On the whole regarding the split more generally I have a couple things to say:
- The cylicalism is always amazing, they all line up perfectly with an obvious playstyle and present new ways to play; all look very satisfying to play as for that reason.
- They all do a good job of representing things that are very difficult to portray in civ. Lawmaking, plundering, stability, stuff like that is way outside of the base mechanics but you still represent them well; so great stuff there.
- None of the original firaxis uniques used. I try to find a place for them usually and its often quite good fun to try divvy them up between the civs. Its also something people recognise as being characteristic of a civ split; see India and Polynesia. I think it also just works - some of my favourite splits are the ones that use the original uniques to their full effect. They don't actually need to have the exact same abilities as vanilla (see India and Polynesia, again.) but its nice to try use them anyway.
- A lot of situational abilities. Sometimes its nice to have some passive bonuses which will nudge you along even if you don't stick to a perfectly straight path. For example Merodach-Baladan is useless if you don't lose all your cities 
Hope some of this is useful and I don't come across like a complete knobend for criticising too much!
International Trade routes to or from a city provide a small
growth bonus and generate +1
gold for every 3
tourism in the home city. +5%
culture in this city is converted to
production of
Capital.
combat strenght.
great people generation and +1 
Science and +10% 