I have the 400/2.8 and find it to be Very sharp, some say it is Nikon's sharpest lens, right along with the 300/2.8. I have used the 200 - 400 and find it to be a very nice performer, but not at the same level as the 400 & 300 2.8's, although it is nice to have the zoom capability. I use the TC-14eII and TC20eIII on my 400, usually stopped down 1 stop and it is a gorgeous lens. The 200 - 400 can be used hand held, for a while, where as the 400 maybe for about 3 shots, then it has to be on the tripod, it is a beast in the weight department.
This is one of the classic difficult choices. I wrestled with this one for a long time and finally went with the 200-400 for the versatility. However, I also have the 500f/4 and the 600f/4. These are all great lenses and you can't go wrong with any of them.
It really depends on what you are shooting. For birding, the 500 f/4 might be a better choice and it is lighter and cheaper than the 400 f/2.8.
I will be going on an African photo safari in November and the 200-400 will be my main lens for shooting the lions and tigers and bears, there is no substitute.
I was on an African safari last Aug. I was stressed about what glass to bring. I shot a D800 with a D300 as backup.
My 600/f4 is heavy and hard to transport, but I'm VERY glad I brought it. Over 80% of my shots were with the D800 & 600mm combo. 15% was D300 & 70-200/f2.8. And some landscape with my 24-70. Wide angle zoom, regular primes and teleconverters never came out of the Pelican case. Tripod was also a waist.
If I had a 200-400 I may have wanted it on a second body, but would not have wanted to give up my 600.
I have the 400\2.8 and have shot birds and some motorsport with it. I had the same concerns when I was deciding what longer lens to get, well 2 years into this experiment and I don't feel like I made a mistake. I love how sharp it is, even when used with TCs. I have a 70-200\2.8 that I use to fill in below 400mm, so with a 70-200\2.8 and 300\2.8 you should be in great shape. A little about me, I prefer IQ over convenience, do not shoot for a living and am patiently waiting for a D300s/D2x replacement as there are 2 ways to get pixels on your subject.
Will shoot for fame...fun...food... a heck I'll shoot anytime anywhere.