As a great man once said, "it's a strong feelings kidney, whichever way you slice it". I'm at work so can't check those clips above, but to my ears there is definitely an extra kick from the slabs - which weirdly was carried over to Frankenstein so I'm starting to believe it is all down to the neck.
I've got Barry Matthew's Slab book and nearly all of the owners (or previous owners) interviewed seem to agree that they had that 'edge' tonally over the standard Precision of the time.
There must be a way of organising some sort of test - same rig, EQ etc, standard Precision up against a Slab. Maybe suggest it to your friend Craig, Slab66?