Can't beat malthumb's answer since he owns exactly the kind of basses you're asking about, but it is a kind of funny question.
A regular MK Deluxe will sound quite different than a Series bass because the signature basses don't have Series electronics. That means humbuckers instead of the two single coil Series pickups with canceller. Mark King was playing a Series bass, not a MK.
The Series semi-hollow construction makes the basses sound really different when not plugged in but I don't know that they would be that different amplified. The sound is dominated by the thru-body neck structure anyway. I seem to remember Alembic saying that pretty explicitly when I had my first Series built and went to the factory to pick woods - the neck woods matter a lot (not in my case, as this was a graphite neck bass), but the body woods were sort of paint. I don't think that was meant to say there was no effect, but that it was subtle compared to the neck structure.
The Series body still has a very thick top and back plate (must be 3/8), so the acoustic effect is pretty minimal. Both the cut out areas are pretty filled with electronics as well. I don't know about malthumb's custom, but by the time you route for the second circuit board, even a solid body instrument is getting pretty hollow. Of course, that wouldn't be the case with the humbuckers.