For backup of all your GNU/Linux system, use Remastersys
It can make a full system backup including personal data to a live cd or dvd that you can use anywhere and install. It'll create a ISO image compressed.
What happens with drivers?
Things like the graphics card and other hardware will be configured and setup automatically and you do not have to use identical hardware. But there is a problem with the Nvidia and AMD proprietary drivers so they will not be available on the live system and will need to be reinstalled after installation of your custom system.
Size of ISO
The maximum single file size for the ISO to be set at 4GB which means the entire compressed.
Where I can burn?
The ISO can be easily backed up to a dvd or external portable drive and copied back afterwards.
For save only your updates:
Save all the package, files located in /var/cache/apt/archives
. And do a backup of the repository indexes, files located in /var/lib/apt/lists
.
Now in the other computer launch Synaptic and select: File->Add Package Downloaded

Then search the folder were you put the files and open it, accept all. With your repository indexes you will not have dependency problems.