I don't have either of these lenes - I have a 500/4 VR and a 400/2.8 AFS-II, but I have used my friends' 200-400 and 400/2.8VR.
First, for birds 400mm is usually too short. I think I have a TC attached to my 400/2.8 maybe 70% of the times.
For me, the 200-400 is handheldable, the 400/2.8 is not. Not only it is heavier, but because most of the weight is upfront it makes the setup less balanced than, say, the 200-400 or 500/4. My friend can handheld the 400 without problem, but he also bench -presses 250lbs 3 times a week!
I think the 400/2.8 is sharper at f4 than the 200-400 at f4. At F8 I think they are about the same. At f2.8 my 400 is a bit soft.
The 400 works very well wth all my 3 TCs - although it needs to be stopped down for 1.5-2 f-stops to be really sharp. The 200-400 works very well with the 1.4, OK with 1.7 but not very good with the 2.0.
Again, which is better really depends on what your need is. All I can say is that both are excellent.
Completely agree. They are both great lenses and I believe it comes down to which one you need or can gain the most benefit from. I have the 200-400 and like it very much as the zoom flexibility comes in handy for me. I'm sure the same could be said by the owners of the 400mm....400VR pros: a stop faster, sharper at wide stops, better with TCs, has VRII
400VR cons: bigger, heavier, not a zoom, more expensive
200-400 pros: smaller, lighter, is a zoom, as sharp stopped down, cheaper
200-400 cons: a stop slower, not as good with TCs, has VR not VRII