One initial remark is that I use the IIIc or IIIf indistinctly so I have the same pictures for both. No big improvements compared to the Leica II unless the slow speeds going down to 1s. But it is a bit bigger and a bit heavier. It is a beautiful design anyway. I use them with a Summitar 50 f2 or an Elmar 90 f4. One thing that is not so common nowadays but that is very convenient is the concept of colapsible lenses. These 2 cm you gain can make a difference when you want to put the camera in a suitcase or something like that. Mainly if you are the kind of person that always want to have a camera with you.
For more information about Leicas: try Leica Company Site
But if you want to go really into it don't miss Camera Quest

Here an advertising published in U.S.Camera 1951 with a prize winning picture taken with the Leica IIIc and the Elmar 90mm above featured. It is interesting to go through the 'advantages' of the Leica IIIc highlighted in this ad.