Traditionally, 64-bit computing is a mixed bag. You gain additional precision and the ability to address more memory, but in many cases those advantages are outweighed by the fact that the 64-bit code requires more memory and cache and the actual individual operations are slower.
X86-64 is somewhat different in this respect, because when AMD took it upon themselves to add 64-bit capabilities to x86, they also made other enhancements including, notably, doubling the number of general purpose registers from a paltry 8 to a more manageable 16. The caveat is that only 64-bit code can have access to these new registers.