The rules are rather simple:
- When restoring a non-detached collection backup, you must restore to the same version. TFS will balk if they're not at the same level. An upgrade will change data structures and stored procedures.
- When restoring a collection that has been detached you can restore and attach it to the same version or (most) newer versions (there are limitations, for example: 2012 rtm and 2012u4 can be attached to 2013, but TFS 2012u1, 2 and 3 cannot)
- You cannot restore a backup from a higher version on an older version of TFS. You must first upgrade the target server.