Frankly, it's not clear to me. The high-level info on the MS site implies that Pro only adds the following features:
- Run many Windows XP productivity programs in Windows XP Mode (separate download).
- Connect to company networks easily and more securely with Domain Join.
- In addition to full-system Backup and Restore found in all editions, you can back up to a home or business network.
That said, experience has shown me with XP that there may be other issues under the hood...like support for SAMBA and NFS in Pro and not in home...which I need for my media streamer. That said, with XP, there were ways to hack home premium to install MS NFS support...and I acknowledge that these issues will probably not affect 99% of home users.
My opinion - if you are getting them for the same price (e.g., $30 student deal), I would go for the Pro version, but if you need to pay more for the Pro version and only plan on using the PC at home (as opposed to in an enterprise), I would stick with Home Premium.