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Having owned and used both, I would highly recommend buying the 70-200 f/2.8 and passing on the 80-400. Image quality is much better with the 70-200 and it focuses much faster (the 70-200 is AF-S while the 80-400 is not; both lenses have VR).
The best two Nikon zooms I have ever used are the 17-35 f/2.8 and the AF-S 70-200 f/2.8 VR.
Those two lenses (the 80-400 and the 70-200) serve very different purposes. Your own needs would determine which to get. I own the 80-400. I don't shoot sports or very much action. My purpose is to get long focal lengths with compositional flexibility, in the most portable package possible, without needing rapid focusing or low- light capability, so it works great for me. Optically the 80-400 is a fine lens.
I own both the 80-400 and 70-200 f/2.8 and find that I use the 80-400 much more. Optically, the 80-400 is a fine lens, and because of its compact size, is easier to take on a trip. As stated before, the focus is much slower than the 70-200, but for low action shots and even for larger and slower birds in flight, I haven't found the 80-400's focus speed to be a hindrance to obtaining the shot.
I'm fortunate to own both these lenses and must admit I tend to favor the 80mm-400mm.
I have some super sharp images from this lens, and have even used it with a 2x Teleplus converter in good light to capture some shots of Tigers at a zoo.
In all fairness though the AFS 70mm-200mm lens does focus a lot faster even when fitted with the Nikon AFS 2x converter.