It's certainly a fun comparison, isn't it Scott ?
There are so many abbreviations these days, you somehow seem to get lost in them all....AFS IF ED IS VR.... Sometimes I think they only make the new lenses longer so they can fit all the abbreviations onto the side of the lens
I'd be fairly confident that the Sigma 70-200 would not be "as good" as the Nikon, but the real difference, I guess you'd need to compare for yourself.
Everyone will have differences of opinion. I have the Sigma 70-300 APO and I think, for it's price, it's a pretty reasonable lens. I've never used the Nikon equivalents, but there are arguments for and against all these lenses. The same would apply for the 70-200's.
Usually, you get what you pay for. Do Nikon make the best lenses ??.....most people here would say "yes". If you believe this to be so, then there's the answer. Does the price difference justify the quality difference, between the two lenses ??.....only you can decide that (as it is a personal opinion, not a factual one).....IMHO