I thought I posted an answer to this, but it never came up...maybe I pushed the wrong button?
I have all three of these pieces (the 80-400, the 70-200 f2.8 VR, and a Nikon 1.7 teleconverter.)
The 70-200 with the teleconverter is IMHO somewhat sharper than the 80-400, and, for most of its zoom range, slightly faster. Without the converter, the 70-200 is one of the best lenses Nikon has made, and is notably sharper. With the converter, though, the 70-200 only reaches out to 340, so it's shorter. The current Nikon converter doesn't work with the 80-400.
Physically, the 70-200 with the converter feels to me to weigh about the same as the 80-400, but is ridiculously long (10 1/8 inches with the converter attached.) The 80-400, when retracted to 80 for carrying or packing, is a couple inches shorter than than the 70-200. It is a bit fatter.
A D3 or D300 (especially the latter, in good light) with a 70-200 would be an awesome hockey shooter, although you might have to zoom with your feet...shoot from right behind the net, etc. It's not long enough for football or soccer. The combination of a D3 with a 70-200 would be the best night combo you ever used.
On the D3, the 70-200 vignettes noticably at f2.8, thogh you can clean it up pretty easily in Llightroom. or other photo processors.
I'd have to say that the 70-200 would be a little short for surfing. There, you really need something a bit more exotic, and the 80-400 probably wouldn't do it, either.
JC