When it comes to this type of lens 70(or 80)-200mm and f/2.8, my preference(and hence recommendation would be(in order of preference):
Nikon's VR, Sigma's (non VR)version, Tamron's version and lastly Nikon's 80-200mm
I have the Tammy, and mainly use it more for static type uses .. landscapes/abstracts, and other tripod mounted situations, but when handholding, it's the VR that I really want.
For a long time I used it mainly for this purpose, and may have used it handheld for 1% of the instances where I have used the lens.
The problem is of course that the VR does give you an advantage, and if this helps you with your style of photography, then it makes you a better photographer!
Not that long ago, I did a couple of shoots at a go kart track with the lens, and found that in doing this handheld I think I missed not having VR for those times when I think I needed it.
If a lens has the ability to make you a better photographer, then do everything you can to secure a copy of that lens as part of your gear list!
I'd say the Sigma lens is also a handy device, simply due to it's better focusing system.. or more accurately it's more user friendly focusing system compared to the Tammy. The full time override functionality of HSM(AF-S) type focusing can never be dismissed.
I think the Tammy has better overall IQ, but is let down by it's clunky focusing system, although easy to operate(compared to the Nikon 80-200/2.8), with the massively proportioned focusing collar, it's still not ideal.
The beauty of the Nikon lens(es) .. whether the new or old model, is that VR is a user selectable feature, so you turn it off when not needed, but more importantly you can turn it on when you do need it, and hence it makes you a better photographer for those times when VR helps.
I have no experience with the new VRII lens, nor the Sigma OS version, only had experience with the Tammy, Nikon VRI model and the non OS Sigma lenses, and while the Tamron is probably 90% as good as the best copy of the Nikon VRI lens, the non VR element has only recently become more of an issue for me.
Up till that time, I really never used the lens other than for still life purposes, and VR never really fitted into my needs as a feature.
I've dismissed the Nikon 80-200/2.8 as the least option, only for a few reasons:
1. the purchase price is higher than the Tammy and Sigma, both of which are equal too or better in IQ terms.
2. again both of the other lenses are better in terms of their focusing systems. Whilst the Tamron is not ideal, it's still better than Nikon's 80-200/2.8 focusing system(unless it's a second hand AF-S model).
3. 80-200/2.8 requires the use of a front filter.. dare I say it a UV/protective filter, to seal the lens against the elements. Without it, you would probably get a bit of dust and other foreign matter in the lens over time. Not bad, but not something you want to deal with in a few years time.
80-200 is a good lens, but nowadays there are better alternatives unless you really do have to have a Nikon logo on the lens.
If pure IQ is the highest priority, then I'd change the order of preference by switching the Tammy and Sigma lenses around.
I think a well focused and steady shot made with the Tammy is going to give the Nikon lens a run for it's money... but you need to be steady as tripod and good with your focusing ability.
Even tho this may sound like a major negative for the Tammy, it's not really if you know your own shooting style well enough to be positively decisive.
For many years, I'd never really used this type of lens handheld all that much, in fact I hardly ever used any lens handheld all that much.
If I was to single out any lens for handheld work more than any other it'd be the Tammy 28-75, and usually for portrait stuff.
When I got the Tammy, many years ago, I had good reason to do so. Years later, my uses changed, and hence my needs changed. Took me about 3 or 4 years to figure it out, but I finally realised what I really wanted the lens for.. in the end I got the wrong lens