I own both (or at least almost - I have a Lawman MkIII). The 357 is a much finer revolver, but the MkIII is probably the more robust gun.
The 357 has the traditional Colt lock work. As long as it is in proper timing, it is a fantastic gun - I actually sold off my Python, but kept my 357. The problem is, if you need work done on the gun, it should go back to Colt because there are very few gunsmiths that have an inkling on how to properly time a Colt double action revolver anymore. And although I never had a Colt go out of timing, I don't shoot any of mine that much. I've also seen quite a few old Colts that did have screwed up timing, so it has to happen to somebody.
The MkIII was Colts attempt to reduce labor costs and eliminate the specialists needed to assemble their revolvers. The King Cobra is the top of the line version of the MkIII action. These guns have been shown to be quite robust over the years. They do not have the "bank vault" lockup of earlier Colts, which is probably why they did not catch on so well when they first came out (the rise of Wonder 9s also had something to do with it). There have been some complaints of broken firing pins from dry firing, so I would consider that a no-no.