Since this hasn't been mentioned yet:
64Bit not only allows you to access more RAM in the OS, but also allows each program to access more than 2GB of RAM. This is a necessity for certain applications.
The differences in the overall architecture go MUCH deeper. 64bit computing allows for wider registers, higher order addressing (like with the RAM), more accurate precision computing (64 bits of precision is a huge leap up), more complex instruction sets (in some cases less), and much, much more...
Windows XP is based off of the NT family. Vista is more of a re-write than a decedent of those two.
This article
here is older, but pretty well written.
Not necessarily.
Twice the data calculation is correct for the most part. But, that double wide data is in some cases (depending on the CPU) calculated in a 32bit register which results in a fairly significant performance hit. In modern CPUs, all those 64bit instructions (and data) are crunched in the same general manner as 32bit instructions. It's just that the 32bit instructions don't fill the entire register or data path. In a sense, running 32bit instructions on a 64bit CPU is wasting half the processing space. The instructions still process in roughly the same amout of time, though there are exceptions.