I had that Sigma 12-24 even back when I still had a 35mm film body and was never really happy with it. Of course, the difference in angle of view between 12mm and 16mm on a full frame camera is rather noticeable. It's about an extra 15 degrees.
The 16-35 is not so bad at 35mm in the corners. 16mm corners is where it is really lacking, but they are just the corners so it really depends on what you are shooting. It's actually not so bad at 28mm at F/4. The 14-24 mops the floor with it, though, and I have the suspicion that I'll have to resort to using a 14-24 on the D800 alot more than the 16-35. Guessing here but on a D800 with shutter speeds below ( maybe 1/30th at 14mm or 1/60th at 24mm ) without a tripod the 16-35 will probably give you a better shot than the 14-24 due to how it handles camera shake.