do you need the versatility more than the speed?
I had the Nikkor 180mm f2.8 AF and really loved it. it was one of my favorite lenses along with the 300mm f4 AF.
that being said, I sold the 180mm when I picked up a 70-200mm f2.8 lens.
not exactly a great comparison since I was keeping the aperture range, but that small bit of extra aperture mattered more 10 years ago when I did it compared to cameras now that handle low light so much better. I imagine that except in more extreme lighting conditions the 80-200 f/4 will not be such a huge light downgrade with a newer camera with good low light performance. I doubt you will be giving up much, if any, image quality by dropping to an f/4 lens. especially if you are using a modern FF camera.
You might want to develop a lens strategy to help what glass to purchase. Where you start depends on what you shoot, but many follow the strategy of buying the trinity [12 (14)-24mm f/2.8, 24-70mm f/2.8, and 70-200mm f/2.8)], which takes care of most anything you will want to shoot except for wildlife / birding, where you will probably want to add a 200-500mm f/5.6 before the trinity. If you are into macro photography, a 105mm f/2.8 will do the trick. You will probably want a 35mm f/1.8 and/or 50mm f/1.4 for indoor low light situations. If you are into astrophotography, probably a 24mm f/1.4 or f/1.8. That pretty much covers the waterfront except for specialty lenses.
That is a tough one. I have a 300mm F4 and a 4-5.6 100-400 and deciding which to take can be tricky. That latter is much newer so it is super sharp and the autofocus is very sharp. Of course the former sits right inside the zoom range of the 100-400. Having said that, if I could only take one and had no idea what I was shooting, I would take the 100-400. It gives up half a stop at 300mm but is much more flexible.
I've always owned a 180mm f/2.8 AIs, but just recently found a nice copy of the AF 180mm f/2.8. I also own the latest 70-200mm f/4, along with the Sigma 70-200 f/2.8. When I want to "travel light", I like the 70-200. The 180mm f/28 AF is just getting "broken in" with my D610 and D750 cameras. I just ran a roll of EK 64 through the F100 and the 180, so I'm looking forward to seeing the results.
I sold my copy of the 80-400 f/4, in favor of a bigger 200-500 f/5.6.
Thanks everyone for the good suggestions and endorsements. I'll try to respond generically to everyone.
Here's the dilemma. I love the photo results of the 180mm and appreciate the f2.8 in lower light, but I'm considering the 70-200 f4 because of the flexibility of a zoom. I'll probably use it more plus the VR will help in low light. It's size is not too much worse, only 1.5" longer and slightly heavier. For those who have suggested the 70-200 f2.8, it's too large and expensive for my taste.