I think the 300 f/4 AFS is a little sharper - its as sharp or sharper than my 200-400 which is sharper than the 80-400. The 300 f/4 is probably a little sharper with a 1.4 teleconverter, but it gets close.
What the 80-400 provides is flexibility - and it provides VR. So as an all purpose long lens, it is probably a better choice. Image quality is still very good - just not equal to a prime like the 300 f/4. The redesign of the 80-400 has created a remarkably fast zoom. While the earlier version - and most alternatives - move to the narrowest aperture pretty quickly, the new 80-400 only is an f/5.6 lens at 380-400mm.
I'd look at the rest of your kit and what you are trying to accomplish. In my case, I have the 70-200, 300 f/4, and 200-400. As a travel lens the 80-400 would replace all three of these lenses. It's perfect for someplace like Denali where space is at a premium - or on the water in a canoe. It's a great lens for hiking and portability. On the other hand, I'd probably prefer the quality of the 70-200 and 200-400 for places like the Smokies and Yellowstone. And I can use a range of options for places like the St. Augustine Alligator Farm depending on my choice of subject.