I'd also be interested in knowing if the battery is more massive than the iPad 2's. A lot of battery "tech" is in the electrochemistry, and if there isn't a significant difference in mass between the old battery and the new one, then Apple's gone to a more advanced LiIon chemistry.
While it's certainly likely that making the board essentially single-sided kept the overall thickness down, it also speeds manufacturing and improves reliability, thus keeping production costs down.