I have both mkIII bodies, so I guess I'm qualified to comment. First, I'll say one advantage of the 1DmkIII is the higher flash sync speed. This is not trivial for someone who needs it. The other advantages of build quality have already been mentioned.
The 5DmkIII is my most used camera, but there are situations I still love to use the 1DmkIII, often for use when I need the extra sync speed. But also to keep some of the shutter count down on the 5DmkIII. They both have dual card slots, so that is important to me. For that reason, the 1DmkIII is my backup for the 5DmkIII should it ever need to go to the shop.
It's a matter of what works, the 1DmkIII has excellent IQ, quite good enough for most all situations, except where very high ISO or extra MP for cropping is desired. When I get a good 10MP image from the 1DmkIII, there is very little I can't do with it in terms of printing large prints, etc. So bottom line, it's functionally very useful, and is very pleasing to use.
Would I sell it to replace it with another camera? I've thought about it, but for the money I can get for it, I don't think it's worth selling. I'd rather keep it than sell it for what they are fetching these days. I agree with the original post, dollar for dollar, the two MKIII cameras are pretty much on par with each other, given that the older camera is valued on todays market at less than half what the newer camera sells for. In my opinion, it's well more than half the camera.