64s can handle 32 apps better than 32s can, and 64s can support 64-bit programs and applications, while none have really been officially released yet, if you're going for a gaming processor to not have to upgrade for a while, go AMD 64-bit.
64Bit reads twice as many bits of data than 32Bit CPUs.
64Bit will remove the 4GB Vitrual memory limitation that is right above our heads. Then you can use that 512MB gfx card with more than 1GB system memory and the PC will be able to access it all.
As for who's 64Bit CPU will be better...
AMD designed how 64bit would work with the X86 architecture. Intel copied the main instructions but did not do everything AMD did. Just looking between the two, AMD's is a more complete design.
As for performance, part of AMD's 64Bit design was adding more registers to the CPU which save instructions for the CPU to perform. That will increase performance while Intel decided not to add registers.
AMD of course has the onboard memory controller and other advantages that will still be there.