64bit windows is only different a way how memory is handled, it should be more efficient and windows is able to allocate more memory. there shouldn't be a lot of backwards compatibility issues, but it might bring some in special cases
but to be honest, 64 bit versions of os are pretty much useless right now, it will have a bigger importance in future
you can see which version of windows you have when you right click My Computer icon on the desktop and select properties
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