This weekend I did my backup/restore the new way. With frolic's RSYNC on both machines, I first copied everyting new from my olive2 to a map BU where I had mounted the data partition of one of my external backups.
rsync -rvua root@10.1.1.36:/data/* /bu
Next I did the same from the BU (BackUp) to my O_Live:
rsync -rvua /bu/* root @10.1.1.35:/data
I had to make sure that the both kept alive during the transfer, but that was no problem.
After this I rebooted the O_Live, and -sigh- it booted without hesitation.

But the library seemed empty, no space seemed to be used by it, no tracks, no albums were shown, in short, a deep silence fell in.

To make a long story short, I had also to rsync the /cfg (5. partition) to the other side. Numerous cache files were transferred, which I don't see as crucial, but maybe some other crucial file jumped over as well. After rebooting this time, everything was fine again.
SIGH
Well, at least I am convinced now, that the music is dependent from not only the contents of the /data map, but also of the /cfg map.
And I hope I will save someone some trouble with this.
BTW: the files ZCFGDB and ZPROFDB should be left alone, and not overwritten on the target, as they are unique for the unit. (Sure, I overwrote them of course)
PS: anyone with an Olive 0xHD tried
http:///builtDhtmlx.php ?