Nikon D600 With Nikon 70-200 f/4G ED VR AF-S or sigma 70-200mm f/2.8 EX DG OS HSM

I'm new to dslr. I'm looking for a telescope zoom lens for my new nikon d600

I read tons of reviews, and I believe these two lenses won't break my bank and has relative good performance. :-).

Both lenses are brand new in market, so I don't find any compare in between these two guys.

Anyone has these lenses and willing to share their experiment?  Any photos took with d600?

By the way, I'm not sure sigma 70-200mm f/2.8 is fully compatible with d600 or not. Nikon has fx and dx, and what they called by sigama?

I believe Nikon 70-200 f/4G ED VR AF-S is 100% compatible with nikon d600, right? Tell me if I'm wrong.

Thanks!!!