The difference: XP-32 use an old technology called 32, XP-64 use another newer technology called 64 ...
The better: Of course newer technology is better (faster), but under some scientific conditions ...
The processor: You may find the version of your processor whether it's 32 or 64 from the manual that comes with your pc, or you will find it somewhere, generally if your windows is XP-64 then your processor is a new 64-bit processor, otherwise, you should look in the manual or in "My Computer > Proprieties" to know which version your processor is.