It's worth noting that we can already do 64bit Ints, but that they are broken up, and hence take a speed hit. By moving to a 64bit architecture, they can be handled "natively", which effectively means they can go faster, and not require any special trickery.
The other major change is at least as far as the x86 architecture goes, 64bit mode adds 8 more general purpose registers(GPRs) to the preivous 8, giving us 16 GPRs. x86 is considered a "register starved" architecture, so the additional GPRs allows for another speed boost, by allowing the computer to keep more stuff on hand at once, and reduce the amount of swaps it needs to do.
PS Can someone confirm the FP thing? I could have sworn most floats were 80 bits