Read this excellent article on the subject:

http://www.winsupersite.com/showcase/winvista_ff_x64.asp

It comes down to compatibility. Unless you're going to be doing some serious computation with huge data sets, and have already checked to make sure all your components have 64-bit drivers available, stay with 32-bit for your own sanity.

The advantages of the 64-bit version are pretty much moot for a home computer.