I'm glad you put your cards on the table, Mark. I was wondering where you might be going with this poll.
I haven't owned a Leica M, just a Minolta CLE and Hexar RF. The Hexar in particular I like a lot ... but it's such a different beast to the IIIc that I can't really say LIKE one more than the other.
The Barnack has that mechanical-jewel feeling that neither the plastic CLE or the techno-wizard Hexar have. The shooting style is much more slow and deliberate, which is no bad thing. You don't want to change lenses with a screw-mount Leica - or Bessa R. M-mounts tempt you with quick swaps, which can be good or bad depending on the circumstances.
I'm preparing to do some photography at a friend's wedding: I'll use the Hexar because it handles so much faster. But a few weeks ago I went around and photographed a street art festival here in Toowoomba, and for that I took the IIIc and a MF RF.
I do think it's worth posing the question as you have: either/or. I am happy with an uber-modern M (compatible) and a Barnack because they are so different. A mechanical Leica M and an Barnack wouldn't differentiate enough for me to keep both. But I don't know which one I would keep. I can tell you that I kept the IIIc and gave away the Bessa R. I didn't mind the plastic body, but the Hexar was all the bessa was and more so I wasn't using the Bessa.
I could be talked into letting the CLE go but it has it's place in the ecosystem: my 40mm lens lives on it.