I've tested the 300 f/4 against the 200-400 at 300mm and at 400mm against the 300 with 1.4 teleconverter. I found in both cases the 300mm lens was sharper. And the 200-400 is sharper than the 80-400.
It makes sense that a prime lens is sharper than a zoom. Most primes are sharper than zooms, and the telephoto lenses are all very sharp. It's really an unfair comparison.
But the 80-400 and 200-400 provide flexibility, and that is a significant advantage. Filling the frame or leaving enough space can turn an okay image into a much better image. I'd consider the lenses alternatives for different situations.
My guess is if you have both, the 300 f/4 will get a lot less use and the 80-400 would be your "go to" lens regardless of a slight difference in sharpness.
I think the 70-200 Ver 1 is the weak link in your kit. The vignetting and sharpness are weaknesses compared to the newer 70-200 on FX bodies.