From an end user point of view, it's the networking features, which you may or may not need.
However, from a Professional view, Windows XP Pro is the final product from the Microsoft "Whistler" betas. Then they took Pro and ripped/disabled various elements inside, gave it a once over and released it as a "Home" version.
You could say that Home is a crippled version of Pro, on that basis I advise everyone to go for Pro, even if in the short term they do not need Remote Desktop (use your PC remotely) or need to add it to a corporate network.
Also, no one has mentioned the other two versions, Tablet and Media Centre.
Tablet is a touch screen version, installed on tablet laptops, that typically have a swivel screen that folds down with the screen up. You can then use a stylus to write or draw onto the screen.
Media Centre, is pretty much a waste of time in my opinion, especially when done on a laptop. It consumes more memory so there is less for your applications (the same with Home, but more so, leaving Pro as the most efficient of the bunch), basically this version is like Home but with the remote desktop and a big pretty interface for viewing media such as photos, videos and whatever you've recorded off your TV/Sat link into it.
This is pointless as most people use either a DVR or their Sat/Cable box includes it, and if you want to keep items, you'll record them to DVD using a DVD Recorder or if you're behind the times a VHS Recorder, NOT your PC which Microsoft has locked up so you can't transfer recordings.