Windows Home Server's home computer backup feature isn't designed for system migration scenarios. If you restore to identical hardware, all the drivers will be correct. If you restore to hardware from a different manufacturer, you're likely to encounter a wide range of problems. Most likely the system won't even boot without intervention.
The recommended course is to restore your data files from backup, and to reinstall programs and recreate users on the new computer. Think of it as a golden opportunity to get rid of many GB of software you haven't used in a year. :)
I'm not on the WHS team, I just post a lot. :)