To me, the worst designed is possibly Babylon:
In vanilla, the UU is tolerable, but in G&K the UU is obsoleted quickly (even on Marathon, CBows appear much too soon, depending on how you tech). This problem is compounded by the fact that the UA gives you extra science. Thus, Bowmen go obsolete probably at the fastest rate of all units in the game. Really, this isn't so much a design flaw as a failure to re-design the UU for G&K. Again, in vanilla, Bowmen have some purpose. But in G&K, they really should have been given a promotion that carries over as they upgrade since they can be upgraded so quickly.
The UB is a joke. Depending on how things go, I sometimes don't build walls at all. Even if I build them, the Walls of Babylon add a tiny bonus to city-bombard damage (which is possibly an okay bonus if you picked the pantheon for city-bombard damage being increased by 30% or whatever, but the AI tends to pick that belief very quickly for some reason, and other beliefs are probably more worth-while in the early game). And the boost to city health (a little more than a standard wall), is more of the same.
Only the UA is really all that valuable, but it's incredibly passive. Basically, I plant that first free GS, then I try to maybe build Leaning Tower and National Monument (or whatever it's called) and get GSes to burn down the line to bulb techs. That's it. The decision-making with the UA is very, very basic.
Babylon being a DLC is even more of a design flaw. Korea is far, far better in terms of having effective defensive UU's, and the boosts for specialists, for finishing science wonders/buildings in the capitol, and for planted Great People are possibly just as good as Babylon's super-early GS if you can go tall quickly enough. Babylon should have been part of the initial launch, and then Korea could be the DLC that basically out-shines them and encourages customers to plop down more money. Why Bablyon was also a DLC is beyond me.
I really vote for Babylon. Between them and India, it's close, but India was there at launch, has uniques that aren't obsolete immediately (the UB gives gold once you go way, way down the tech line to get Flight), and has a UA that really makes you have to calculate how to get a lot of food to use it well (which sometimes takes a little luck and/or rerolling). Babylon's UA is powerful but boring, and fades away later in the game, and the UB and UU are absolute afterthoughts almost every single game as them. And Babylon, from a design standpoint, competes directly with another DLC, Korea, and really fails to offer something different enough or good enough to justify getting both DLCs except to have all content available to play with. If I was on a budget, and/or was less of a fan of the game, I'd probably not have gotten Babylon at all.
