I have both. Both are in flawless mechanical condition.
The M3 is an improvement in many ways over the IIIc.
But does "improvement" mean "a better experience"? Ummmmm.....
Op ed:
Not really.
The M3 is easier to load. Barely.
The M3 fits my hands better.
The M3 takes brand new lenses.
The IIIc fits my pocket better.
The IIIc is more socially disarming and friendly. And the M3 is already socially disarming and friendly.
The IIIc gets used more.
3 Barnacks price out to 1 M3 here.
Both are easier to operate than getting in a car, starting it, and safely backing out of a parking slot.
Basically it's this for me: if I want a vintage-only camera experience, it's my Barnack. If I want vintage with modern flexibility, it's my M's. If I'm walking about and want no one to know I have a camera, it's my Barnack. But I love both systems. Immensely.
Maybe I'm a blasphemer by saying this but to me, my Barnack Leica gets treated like a vintage Olympus Stylus Epic. I can bring it almost everywhere. Only it is orders of magnitude better in quality/durability.
My M's are, well, M's.
If I had to use it daily? M series all the way.
That's a couple cents worth more.