NO, not unless you have a very compelling reason to NEED a 1 series body the 5D MkIII is a much better camera. Better AF, better ergonomics, vastly better iso capacity, better flash compatibility, the list just goes on and on.
I have had 1Ds MkIII's for years, and even I am tempted to sell them to move up to the 5D MkIII's, the very few 1 series features that are unique, whilst nice, are not very convincing when compared to the major features the 5D MkIII has over the abandoned 1Ds series.
Having said all that, the 1Ds MkIII is a very major upgrade from your 1Ds MkII, it was a huge upgrade, battery, screen, self cleaning sensor etc etc.