Problems with Migration Assistant - works with one mac but not the other

I have two early 2009 Mac Mini computers running 10.6.8, a 2008 MacBook Pro running 10.7 and Time Machine backed up onto a WD 1 TB drive with the backup coming from only one Mac Mini and therefore also done in 10.6.8.

-My main Mac Mini started to show SMART failing so I thought to migrate all my files to my other Mac Mini. However while Migration Assitant (MA) would launch, the WD drive is visible in Finder, I can watch a movie on the WD drive using my "spare" Mac Mini, and while after some spinning ball time the backup drive shows up in MA, MA starts to freeze (and in Force Quit window shows as "not responding") thereafter.

I then tried using MA on my MBP runing 10.7 and it successfully transferred the backup files (generated in 10.6.8) so there does not seem to be a problem with the WD drive or the backup files.

I reinstalled and updated to 10.6.8 OS X on spare Mac Mini ("SMM") and tried MA again. Same problem. Either MA on SMM fails to see the back up drive or it if does see it, it freezes shortly thereafter while calculating sizes (I leave on this screen for 20-30 min, on MBP it calculated sizes in few minutes).

So unless I have missed a trick this seems to be a specific MA problem.

Any help would be so gratefully received!