Upload & Sell: On
I'll make it simple for you, pare: 200-400L is more than an effective stop of light slower, it is almost as heavy and as expensive, and it stops AFing beyond 784mm, whereas the 600 f/4 will AF at 1200mm and yield a very good IQ at that.
Out of curiosity, will the 200-400 take a 2X teleconverter without the internal 1.4X activated? If so, it can do 800 at f/8. Still a stop slower than the 400/2.8, and significantly shorter than the 600/4 + 2X, but not necessarily unimpressive.
Still leaning towards the 500/4 though.