Advantages of 1DsIII: better build, better weather sealing, integrated grip (if you like grips), dual CF slots, better viewfinder, f/8 AF (advantage goes away in April 2013)
Disadvantages of 1DsIII: much lower max ISO, AF system not quite as good (but very close), rear LCD not as good, no video
If you need a FF camera that's built like a tank, the 1DsIII is the way to go. Else, the 5DIII is probably the better choice.