OP. If you want to shoot birds, and more specifically flying birds, there is no better lens at any price than the 400 5.6. If you want to shoot "wildlife," then I would recommend the 100-400, or 300+TC options. Both will still work and do well for birds as well, but certainly will excel in other areas the 400 will falter.
Me personally, the 400 5.6 is my favorite lens, and I would never sell it. But I use it for BIF, and that is about it. Everything about the lens lends itself to it, light weight, razor sharp wide open, fast af, easy to maneuver, comparatively compact, long minimum focus distance helps prevent focus searching, no IS since you will be shooting over 1/500th anyway, ect. All this makes it perfect for birds, many of those things will also limit you in other areas. I happen to be a tele-photo-a-haulic, so I have other lenses for those situations.