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.
http://www.microsoft.com/windows/win...e/default.aspx
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.