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 can't 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'm still a bit skeptical of third party lenses but I'm 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'm on a tight budget and own a crop body as well as a full frame.

The f/2.8 is a lot bigger and heavier and will need a tripod or monopod most of the time for best results. The focal length restriction you mention at close focus is something I didn't know about, but given that 200mm will usually be used for distant objects it's really not a significant restriction. Being so large and bulky makes it less than ideal for candid shots; people tend to notice and react when they spot a dirty great cannon barrel of a lens pointing their way.

The f/4 is a better everyday lens and is physically far smaller and lighter. The superior VR allows more handheld shots, and the two stops slower aperture can be offset by increasing the ISO although depending on the body sensor performance you'll either have a bit of extra image noise or a lot more. Shoot in RAW and much of that can be corrected.

The Sigma and Tamron are good value but don't hold their resale value like a genuine Nikon lens. That drop in resale value can make them the more expensive choice overall.

Whenever I'm choosing between alternatives, such as when I searched for a wide angle lens, I make out a spreadsheet or table. I populate the squares with facts about the choices, such as cost, focal lengths, etc. I then use photozone.de to find out the optical qualities of the lenses and put that data in the spreadsheet. One will stand out as the choice for me. Try it.

Avoid the 80-200 f/2.8. That lens has horrible spherical aberration (causes focus shift) which is apparent at close focus distances (less than 15 feet). At long range, it's a good lens, but it is heavy.

The 70-200 f/4 is a very nice lens, but you need to figure out if a f/4 lens will do it for you. That's a 1-stop difference. You can make up for the 1-stop difference in ISO if you're trying to capture sports, but you may end up with a bit more noise in your image due to the higher ISO.

Of course, the 70-200 f/2.8 is a great lens. If you don't mind carrying the extra weight and the extra cost over the f/4 version, then go for it.