Ok... while I'm walking down this road... 400mm or 300mm f2.8L? I have the 70-200 f2.8L is mkii at present. I would need to upgrade my 1.4x mkii to the mkiii and get a 2x mkiii.
That would give me the following:
400mm @ f2.8
90-280mm @ f4
560mm @ f4
140-400mm @ f5.6
800mm @ f5.6
Mmmm... that sounds delicious.
Which lens to go for really depends on budget, long term plans, and shooting style.
The 70-200 II works so well with 1.4x TC's that it can almost render the bare 300/2.8 II pointless for anything but wider than f4 shots. Obviously the sharpness, bokeh and AF speed take a step up, but it's not like they're lacking on the 70-200 II. However, once the 300 II is combined with a TC, the 300 gains a very real advantage.
Therefore, if you go by the adage that you should buy the lens whose native length is what you primarily intend to shoot with, you could argue that the 400 II makes more sense to pair with a 70-200 II as the only big white in your kit.
The 200-400 on the other hand buys you flexibility. It does next to nothing the 70-200 and 300 together with a selection of TC's does, other than allow you to go from 200 to 560 without any messing about with lens changes and adding/removing TC's, and save you a little bit of bulk to lug around. Looking at it the other way, the 70-200, 300 and TC combo does give you an extra stop at 200mm and 300mm, options wider than 200mm, and slightly more reach at f5.6, together of course with a lot of spare change.
Compare the 200-400 to the 400 II, and the cost gap narrows while the prime advantage widens (f4 at 280mm with both, but one stop faster at 200, 400 and all subsequent telephoto lengths).
If I was somehow in your financial position, I'd be torn between the 200-400 and the 400 II.