Unable to boot (kernel panic - reboot cycle) after 10.10.4 upgrade
There is an issue with the backup, corrupted files etc. Instead of restoring the backup use Migration Assistant to copy your user files and (optionally) applications. Once that is restored and you can verify the system is working you can work on reinstalling any system modifications that the Migration Assistant did not copy.

If the system becomes unstable after running Migration Assistant and transferring Apps and user data. Scale back what you copy to just user data.

Yeah reinstalling system mods and apps can be a PITA but it sounds like you may not have a choice as your backup is somehow damaged. Without knowing exactly what is wrong with it you will get your best results by restoring as little as possible from your old backup.