My perspective is the 200-400 is probably a premier choice for larger animals like on a safari for example but it will most likely leave you wanting more focal length in many birding situations.

There are many places where the birds are very approachable....if you are living close to one of these places I am sure you could do great with the 200-400.

I have seen many amazing images made with the 200-400 and would have no reluctance about IQ BUT if birds are your main interest I would go for the 500 or 600 f4 if possible and of course the 400 DO is a killer for flight images due to it compact size and lighter weight.

I don't get to travel much and mostly I image birds from a set up in my yard and even in this controlled situation 500mm is way better than 400mm. For small birds I will often add the 1.4 TC to reach 700mm.