For Sigma, price would be around 1300$ in grey and 1500$ for regular one. Nikon goes for around 1650$ regular
Sigma has very good contrast and sharpness. Very nice bokeh. Build quality is pretty good. Weight is manageable, though a monopod/tripod will be called for in anything less than good light.
Difference with Nikon 80-200mm AFD will be mostly subjective. Nikkor has slightly better build, image quality is almost thereabout and its a bit slower in focussing (Sigma has HSM). Nikkor should have better resale value, though the Sigma also holds its value pretty well (as I found out)
If you can get hold of a second hand one like I did, then you should be happy. Get either of these which is available cheaper. Both of these are excellent lenses, and wont constrain you from taking excellent pictures. Its upto you to make the best use of the one you decide to get.