The increase in the number of double precision capable units directly increases complexity and indirectly increases pressure to increase the size of registers (and number) and memory caches.
The problem with paper FLOPS counts are they are based on your perfect utilisation of GPU resources rather than real life computation. So I can see this becoming a war over shader/gpgpu compiler technology.
THe point being, AMD increased their double precision power also, significantly, yet they don't have a 3.15billion transistor part. Its NOT the reason and I really don't know how to make that more clear. They've not massively or hugely increased the ability to do double precision, its not some new thing only the Fermi can do. AMD roughly doubled the size of their core in terms of transistor count from last generation with double the shaders, double everything else DX11 improvements and better double precision power.
Nvidia have only roughly doubled their transistor count.
Your idea, seemingly, is that Nvidia have massively increased the double precision power of the card, that its somehow exponentially faster than ever before, and thats why its double the size. But thats all it is, double the size, going from a 240sp card, to a 512sp card.... hmmm, wait, it looks to me its the exact size you'd expect simply doubling the counts on the last generation card.
Where exactly is this massive increase in transistors just to do double precision?
It was 50% bigger before, its still 50% bigger, its got entirely nothing to do with the double precision count, if that added sooo much to the size, it would have been far bigger than it is.
Bigger cores, harder to make, worse yields, more money wasted and slower production, its just bad business every which way you look at it. Nvidia have been selling 260gtx's at cost for almost a year, with their exclusive partners leaving left right and centre. most crucially, double precision is entirely and completely useless for gaming, which is still the massive, massive, massive majority of where their sales go.
IN terms of gaming, they may aswell advertise that the pcb will be so large you can use it as a paddle for your boat. Sure, the 5870 can't do that, but its just as irrelevant to gaming as double precision power is.