From what I've analyzed...
If we did get Russia and the Iroquois to declare war on Babylon, they have a much better chance at acquireing more cities. (or razing them). We only have 1 city that borders the Babylonian mainland, and that one is in danger of flipping. It would take 15-20 turns for our productive cities to send over units like muskets and cannons (catapult upgrades that the military has been working on - sort of a modified boomstick). Knights and Cavalry would make it in less time (in about half the time). In 20 turns, They're sure to have Cavalry as well. (BTW, they currently have about 40 units in our borders) Their city of Samarra has Saltpeter, but borders the Iroquois (a prime target for them).
Mainland Border Cities:
Russia - 6 Babylonian Cities
Iroquois - 5 Babylonian Cities
Fanatika - 1 Babylonian City
On a side note - most of our productive potential is "wasted" by foriegn cities around our FP.
Now for analysis on America:
England and France are embattled in a bitter war, which would give us time to move in before they decide they want part of the pie. Plus, our productive cities are so close to their border. They have 2 dyes within range (Babylon has one close to Russia). They have horses in Boston, which is somewhat close to the border and could prevent them from getting Cavalry. (They have saltpeter connected near Washington).
For "building up", I'm going to go with America on this one. They'll have more production... We could go for the west once we have tanks...