It's really going to depend on what you're shooting and how you're shooting it.
The 200-400 is going to be more of a general-purpose jack-of-all-trades type of lens. If you need to shoot at shorter than 400, and especially if you need to rapidly change focal lengths, that's the lens.
On the other hand, f/4 is slow, and f/5.6 (with the TC) is very slow. The 400 doesn't get as slow as f/5.6 until you put on the 2x, and then it's all the way to 800 mm. If you'll be shooting primarily at the long end of the 200-400 range, especially if you'll be using that teleconverter a lot, the 400 will easily be the winner.
In other words, go with the zoom if you're mostly looking for a lens that goes up to 400 mm, and especially if you'll only be shooting in good light. Go with the prime if you're mostly looking for a lens that starts at 400, and especially if you'll sometimes be shooting in questionable light.
Chances are, since you're seriously considering the 400, that's the lens for you.