LAST EDITED ON Dec-30-05 AT 05:12PM (MST)[p]Why too much to explain in a single thread. However, if you want out of the box satisfaction, the 80-400 will be your best choise. From purley a functionality perspective the 400 is better. These are my opinions based on my experience, nothing more, and nothing less.
If you're shooting chess during midday sun, the 500 will work with a tripod and allow you to be a bit farther away so as not to disturbed the "action."
If you want to chase wildlife around in the hills and through the woods, photograph them in less than stellar light like in the woods, and you want good quality color buy the Nikon. The 200-400 f/4 vr afs to be more presise.
back to your question, the 80-400 has vibration reduction (VR) this will help stop the shaking and allow you three stops over normal. The sigma 500 does not have vr technology. Have you ever tried to look through binoculars? You notice they shake a lot and the higher the magnification the greater the perception of shake - its the same with camera lenses, except the 400vr takes the shake out - its amazing technology and it works. It's not a panacea, and its not fool proof, but it will give you 10x the keepers as the 500 sig.
To make matters worse, people that shoot long zooms, tend to use the entire zoom range except everything under maximum. You will find that for the 500 this just means more shake which requires better and more complicated techniques to shoot.
You will have to shoot the 500 sig from a tripod 90% of the time (ever try chasing mule deer around with 10 lb tripod and 3 pound head with the camera and lens attached to it, I think you get the picture). Ask those guys who use it if they can hand hold the 500mm 6.3 at 125 of a second and get a tack sharp image? Impossible with the 500 sig., possible with the 400.
I know why your asking, it's because of that extra 100mm of magnification isn't it? Well, all the magnification in the world wont help you if you cant hold the damn thing still or you cant get enough shutter speed to capture the action. A 500 6.3 used in full light and shot at say iso 200 will capture decent images, soft at 500 due to inferior glass, but decent nonetheless. You will be hard pressed to get usable images with the 500 in low light, especially if you dont use a VERY good tripod and a VERY good head. I know guys will argue with me, but look at their images. In fairness we are not talking about photographing race cars or the like in full sun. the is a wildlife forum so I'm assuming we are talking about wildlife situations.
Anyway, to me it comes down to the actual usability and convenience of the lenses. Dont miss quote me or accuse me of not knowing what I'm talking about. You can get good images with a 500 sig. But you will have to work harder and you will get far more shots with obvious camera shake than you will with the 400 vr. Just look a the armature (this is not an insult it means non-pro) photos on this site and others taken with the lens most are not sharp because of camera shake, the photographers rarely ever approach the lens capabilities because they cant get fast enough shutter speeds or stop the shake, so the limiting factor is in the technique, and not the lens. If you want this lens for photographing wildlife, you almost always will be shooting in dim light, the worst thing in the universe for a slow 500 6.3!
Thats the basics. As a matter of fact, the 400 has better color, less distortion around the edges when shot wide open or at maximum zoom, the colors or more accurate and should you ever have a problem with it Nikon is a much better company than sigma to deal with. Trust me, I have used most of the sigma pro stuff, I eventually gave up on them. I still have a pile of their lenses including a 100-300 usm f/4 that I've never used. I'm not referring to the 500 4.5 or the 300-800 so again don't anyone misquote me, I'm talking about the long consumer sigma zooms.
This may not be what you expected, but it's real.
"Roadless areas, in general, represent some of the best fish and wildlife habitat on public lands. The bad news is that there is nothing positive about a road where fish and wildlife habitat are concerned -- absolutely nothing." (B&C Professor, Jack Ward Thomas, Fair Chase, Fall 2005, p.10).