I disagree somewhat with the above. Not saying you're wrong, obviously you have your own expererience but that may not be typical for all (and especially newer) 64-bit systems. If your system is still that in your signature, it is somewhat aging. Not that its bad but those motherboards and chipsets had early implementations of 64-bit support and the difference with newer systems should not be neglected.
Purely MC, probably not so much. But MC is never alone on a system.
64-bit offers many advantages that MC can indirectly benefit from. On a 32-bit OS, maximum memory is effectively limited to ~3.5GB with user space (the effective memory a program can use) is 1,5GB (total userspace is 2GB but there's overhead and other stuff snooping away from that). Although MC may not use that much, other programs share that same pool. On a 64-bit system user space is not shared meaning each program can use the full 2GB of user space. If a program is specfically written for it, it can even use the full 4GB you can address with 32-bits.
Also a 64-bit system can be faster, whether that is noticable or not measurements and benchmarks have repeatedly shown that it can be considerably faster at certain tasks. 64-bit applications do have a little bit more overhead resulting in a larger memory footprint and yes, some rare cases 64-bit processes can be slower than their 32-bit counterparts. This was typically the case when 64-bit was new and drivers not yet fully optimized. Today, at least on newer hardware with new drivers, things like disk access, memory operations and certain CPU operations are (sometimes much) faster on 64-bit systems. MC can benefit from most of these subsystems.
Typically, multitasking works better too on a 64-bit system too. MC is heavily threaded and should benefit from this too.
Compatibilitywise I don't think 32-bit OS has an advantage over 64-bit anymore (used to be the case, yes), unless you're running very old hardware or outdated drivers/software that have known compatibity issues. 32-bit mode in 64-bit OS is very mature nowadays and I believe its very unlikely that problems arise.
I'd say if you have to ask, choose 64-bit. Not doing so is simply postponing the inevitable.