Unfortunately making a backup to restore to another system with different hardware will always leave you with a half stable / configured system.
The possibilities and variations of hardware and what needs to be configured are huge. The fact that you were able to boot on that backup you restored to another system and only complaint about the graphics configuration is not normal.
Full backups, 1:1 copies or system images are to be restored to the same hardware configuration.
Tar backups wont help you, the chances of anything going wrong if restored to a different hardware will be greater (from what I understood RemasterSys does try to make your system bootable on a different hardware).
Word of advice is, make backups of what is personal. Full system restores work perfect only on the same hardware.
If you want to sync apps between systems and both systems have the same applications installed (same versions would help) a backup of you
home will contain most of the configuration you need to restore, a script can be made that gets the packages from one machine to the other but seriously you know what you use daily, a script reads all the packages from one installation to another would really be a overkill since you would have to sort out the packages that you don't want installed on the other computers (ie: hardware drivers).
If you want to transport packages from one computer to another and be able to easy select what to install use APTonCD for that.
Other then this will need some more (maybe a bit!) of configuration and trouble shoot.