Hi Patrick, great question.
Short answer: I only have the Sigma but would expect the Nikon to be substantially better.
Long rambling answer: Patrick I think that you have to look back ten years when the widest full frame lens readily available by Nikon was the 14mm 2.8 at a substantial sub $3k price. I assume this is because that is what they could reasonably make keeping their pro quality objectives in mind. With the rise of DX format cameras, there came a need for what (on a 35mm) could be called extreme wide angle. These lenses came about by using tricks from telephoto lenses by using things such as a negative lens group to shift the focal point. In a telephoto lens, there is often a negative element after a positive element to shift the focal point (the point where the light rays converge) further back than it otherwise would be. This is used so a 800mm 5.6 doesn't have to be 800mm long and in real life the focal length of such a lens is usually somewhere in front of the front element.
Conversely, one could imagine that for a single element 12mm lens, the rear of that element would be within the camera body! These new wide angle lenses often use a reverse of the telephoto design, putting a negative lens group in front of a positive group, thereby shifting the optical centre well to the rear and creating very short focal lengths. As you can imagine this is somewhat oversimplified and there are also aspherical elements, ED glass, etc, etc involved.
My thoughts on why the Nikon 14-24 would be better is because the chose a focal width (14mm) they already knew they could produce at a pro quality level at a reasonable price, avoiding the "ultra wide" as it was not required on the FX format, also I assume due to pricepoint they are built with better quality glass. I also think their previous experience building this size is helpful. It is also a generation later than the Sigma which was the first of the breed. The Sigma does a very admirable job, but I think that consumers are probably not prepared to pay what would be required to put top quality elements into a 12-24. There is a reason a 600mm F4 costs $13k and a 12-24 costs $1k and it is not just the size of the elements. I think they could produce better quality extreme wide angles, are we prepared to pay? Personally I would love a high quality 10 or 12mm prime which should be cheaper to produce and possibly higher quality.
PS (disclaimer, my total knowledge of light and physics came from staring at the cover of "Dark side of the moon" whilst my friends were stoned)