To me the question is a bit odd. The 600mm is made for a totally different use than the 200-400. They are both exceptional lenses and outstanding for their use. When going on a trip, where I don´t bring both, it has not been difficult to choose which one to bring.
It would be more difficult to compare the 200-400 with the 300 f2.8L IS II, with the 1.4xIII and 2xIII extenders. The 300 is clearly less flexible, but it is smaller, it gives you exceptional IQ, AF speed and a stop advantage and also very good performance with the extenders. You also have significant money saved for something else.
It´s a substantial cost to get both the 200-400 and the 600, but it would have to be for something really exceptional if I were to part with any of them.
A agree Eldar, both these Lenses are a substantial investment for most that decide to buy either, or both, and one would imagine a serious amount of thought goes into that decision.
The 600f/4 is not your close in type Lens, it's uses are varied but going on CR and the many fine Images I've seen with the 600 exhibited here, Birders are the Lenses main stream users, followed by people like myself, Wild Life at a distance.
The 200-400f/4 is clearly more your closer in Lens, with the option to go out to 560 albeit at a small light disadvantage with f/5.6, More suited to your Wildlife/Sports Photographer.
If I'm heading to Open Plains style Geography, Serengeti, Mara etc, I would place the 600 +1.4x in the Bag first, the 200-400 second.
If I'm heading to Okavango Delta, South Africa, Timbavati, it's the 200-400 in the bag first with the 300f/2.8 second.
In my own Imaging if I had to choose just one Lens for 90% of my Imaging, it would be the 200-400.