AIX has mysysb because IBM owns the platform from A to Z. Linux can be installed onto almost anything.... including an IBM Power system.
There are several ways you could do this. One way is to make an image backup of the partitions. You'd still have to lay those out and restore them. Likewise, you could keep partition and boot data and store file archives (e.g. tar). Again, layout and boot you'd have to handle with the captured data.
If you are looking for an "all in one" thing, where the backup does some of the things I mentioned above in a more (or less) automated manner... you could look things like:
Mondo Rescue - GPL disaster recovery solution (there are other projects besides that one that attempt to do similar things)