I owned a 1Ds Mark III. It was amazing how accurately it could reproduce skin tones. I'd say no other camera can get skin tones as "correct" as the 1Ds Mark III can. With that said, it couldn't go anywhere near ISO 800 or higher like the 5D Mark III can. Overall, the 5D Mark III is much more versatile and has outdated the 1Ds Mark III and I probably wouldn't even consider getting one, especially since a new 5D Mark III is often cheaper.
However, it wasn't made to do the same things the 5D Mark III was made to do. That's why I think the 1Ds Mark II and Mark III are both excellent studio cameras. But if you show me a studio photo from a 1Ds Mark III shot and a 5D Mark II shot let's say, you won't be able to tell which is which. The only difference is skin tone. I still can't get over how well those cameras could do.
With a newer, higher MP camera, I'm sure it will be the true successor to the 1Ds Mark III. It'll be 39-46 mp, will be low fps, and low-ISO only.