If there wasn't a difference, they wouldn't bother seperating the two.
If you do a google search, there is a comparison from microsoft at the very top of the organic search.
For the most part, you really only need Home Premium actually. Pro basically adds the remote desktop (which there are better options out there that are free - teamviewer for instance), XP compatibility mode (never have really had to use this anyway and I am running 64bit) and a few other features.
I would save yourself the money and just get the HP.