I have the 150-500 and have used it on my D800. It works just fine. But remember that the 150-500 isn't super sharp at 500 so don't expect miracles. So if you don't have unrealistic expectations you'll be plenty pleased. I'm in the process of selling my 14-24 and 24-70 and replacing it with the 24-120 VR. I expect that will be just fine.
The Sigma 70-200 is very good and you shouldn't see anything wrong with it on the D800.
Personally, I think the "camera sees the flaws" comments are either from nitpickers or just overblown. You'll see your own flaws in photographing (technique, ability, etc) long before you see the lens flaws.