With 64 bit computers becoming mainstream (its hard to find a machine thats not 64 bit capable these days) the question being asked more often is “Should I install a 64 bit operating system or a 32 bit operating system?” While the advantages of a 64 bit OS might be more obvious for those running native 64 bit software, or those who have a need for more than 2GB of memory, its a bit more murky as to whether regular 32 bit applications will also perform well on a 64 bit OS.
A 64 bit capable processor has an increased number of registers, as well as an improved floating point unit (FPU) design with double the number of FPU registers. 64 bit operating systems can take advantages of the expanded register set available to a 64 bit processor. The advantages to this are fewer memory accesses for data that can be stored in registers, leading to faster execution of computationally intensive processes. You can read more about this from this Cakewalk X64 white paper from several years ago.
Here is an interesting benchmark showing that 64 bit windows can perform better even with the same hardware and software. Some of the benchmarks are relevant to digital audio processing as well and so apply to DAW users.