Wildlife & Birds in Flight Photography
Two subjects that require a different approach.
I have both the Version 2 400f/2.8 & 600f/4, and in my own use they are Lenses that I use for different Geography, I'm not a Bird Photographer, having said that, I take Photos of Birds from time to time, but mostly I take Images of Wildlife.
The 400 I tend to use when I know I'm going to be in more Bush type Country, less Open space where I feel I'll be getting closer to my subject, South Africa, Botswana, Zambia, the 1.4x series 3 works great on this Lens, but the 2x I feel degrades the Image so I Rarely use it.
The 600 I tend to pack & take on trips where I'm likely to be working in more Open areas, subjects expected to be further away, Tanzania, Kenya, Arctic & Antarctic. Same applies re the Converters, 1.4x matches well with very little degrading of the Image, 2x very seldom.
Another set up may be worth looking at, the New 200-400f/4 (1.4x), more versatile, Image IQ from reports I've seen indicate excellent, and I've handled the Lens myself earlier this year all indicate that this may well be "The Wildlife" Lens, certainly I have a Pre Order in & expect to take delivery mid June, it's a little short @ 560f/5.6 for a dedicated Bird Lens I would think, the 600 has the reach with the 1.4x extender, 840f/5.6. But up to almost 600 you have a huge amount of versatility, worth looking at if your leaning towards "wildlife" over Birds in flight.
All three of these Lenses are in a similar cost ballpark, along with the 500 mentioned by others, I'm sure it's just as good as the other V2 Lenses from Canon.