As basic as can be, http://en.wikipedia.org/wiki/64-bit:
"64-bit CPUs have existed in supercomputers since the 1960s and in RISC-based workstations and servers since the early 1990s. In 2003 they were introduced to the (previously 32-bit) mainstream personal computer arena,
in the form of the x86-64 and 64-bit PowerPC processor architectures."
If your question is whether XP 32-bit or 64-bit shoud be run...I'd have to answer "neither" at this date.
Windows 7 should be run, with the user having the option of choosing whether it's 32-bit version or 64-bit version.
The big advantage to 64-bit O/S is that more RAM can be installed and recognized by the syatem, while 32-bit O/S is limited to 4GB of RAM.
Obviously, this difference is not a particular "advantage" to everyone, since many users don't do anything that would require more than 4GB of RAM. Combine this with the fact that few applications are written to take advantage of 64-bit operating systems...and I think that's where we are today.
Microsoft had this to say about such, http://www.microsoft.com/windowsxp/using/6...ploringx64.mspx