Nikon mount 70-200/80-200 shootout?

I'm looking for a fast telephoto lens for sports/candid shots.

Obviously, the Nikon 70-200 f2.8 is the most optically superior (although it has an older VR system). I know that it has issues when focusing at close objects (at 200mm it is actually close to 140mm when focused close).

Another choice is the Nikon 70-200 f4, which is lighter and cheaper, but still over a grand. Although it has an excellent VR system (4 stops), it has a smaller aperture which cannot freeze motion as well as an f2.8 aperture can.

I have also ruled out the sigma 70-200 and looked at the Tamron 70-200. I have read positive reviews from it. However, I am still a bit skeptical of third party lenses but I am still considering the tamron.

The last choice that I have is the 80-200 Nikon f2.8 which has no VR and has slightly inferior optics as well as slower AF and has no weather sealing.

I'm torn on which one to choose! Please be aware that I am on a tight budget and own a crop body as well as a full frame.

Thanks

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