I like to think in context of my total kit and likely use cases. For me, the 70-200 f/2.8 is a workhorse lens that I use for landscapes, portraits, events, dogs, and equestrian. I frequently use it at f/4 or faster. With the 1.4 TC, you are covered up to 280mm.
I have an older F-mount 300 f/4, as well as the 500mm PF. Both are relatively compact, sharp, and work with the 1.4 teleconverter. As a result my normal kit is the 70-200 plus one of my longer primes.
The place I would use the 100-400 is for travel, or in place of several of these lenses. I don't think it makes sense to have the 100-400 just for the 280-400mm niche (or 280-560mm if you consider the TC). But for me this is a consistent thought - I have not owned either of the F-mount 80-400 lenses and never missed them.
As a wildlife lens, the 100-400 is a good focal length for large mammals - elk, deer, bears, etc. - and large wading birds. It's a bit short for small birds but is fine with the 1.4 TC. I would not expect it to be very good with a 2.0 TC although it works if you already have that teleconverter. I could see the 100-400 for some sports but it's a little slow and lacks subject isolation of a faster aperture.
Both lenses are excellent for what they do. I think the key is the aperture you need rather than the focal length.
