fx991 You cannot live-migrate between hosts with processors that have different instruction sets.
You would have to shut down the VM and then migrate it and then power it back on after migration completes.
The E5506 and E5620 have similar instruction sets but the E5506 does not support hyperthreading or AES instructions, so there are some differences here.
The E5-2643 v2 is completely different.
If you power off your VM and then migrate it, it should be fine. From what I understood from your post you tried to live-migrate it and then reboot it after it had migrated and run into issues, which I would expect to happen.