How important is vibration reduction on a 70-200 telephoto?
Since the Nikkor is the one your looking at I would assume you can afford it, and if you can afford it then that is the only lens to consider in that category. The glass and build quality of the lens are superior to the Sigma, and Nikkor glass holds its resale value much more than Sigma.
I had the chance to shoot on the slopes for two days last season with that lens and I wish I could afford it along with video gear. I need to choose one!