Really depends on how you shoot.
I use APS-C & full frame with a 150-600 and a 300 F4L. I do tons of birding, weekly pretty much. I go about it several ways, sometimes from a blind up and close, sometimes it's from trails, stalking and walking, sometimes I'm just scouring the shore line, sometimes I just go out to a location in the marsh early and wait for them to come to me. But from my own experience, I went from the 150-600 to the 300 F4L, because my habits shifted me towards using the shorter lens because I found myself working to be closer to the subjects more and more, and so I didn't need the extra reach. Lately I've been using just a 7D (APS-C) and 300F4L IS and that's it. I find it's plenty of reach. A full frame equivalent would be a full frame camera and a 500 F4 to get the approximate field of view and same aperture speed, and that would cost a lot more money. So for budget, I've kept it simple with APS-C and 300mm. I was using APS-C & 600mm from the 150-600 and I loved having all that reach, but I found I was too close after changing my approach to birding/wildlife, and so I didn't need as much reach, so I started using my full frame with the 150-600. I realized I was doing that just so I could still shoot at 600mm for the sake of shooting my 150-600 at 600. Kind of silly, but upon reflection that is what I was doing--justifying the 600mm basically to myself. So I started shooting with a 200mm & a 1.4x TC (280mm). I used it a bunch and found I really liked it on APS-C. So I picked up the 300 F4L IS. And now it's basically all I shoot and my 150-600 hasn't been out in a long time. The beauty of the 300 F4L IS is that it can focus so closely, so I'm not "too close" for use, yet still lighting fast on focus, F4 for speed, sharp wide open, and has image stabilization. If I want more pixels on target, I can throw a TC in there for a 420mm F5.6 with image stabilization as well. And on APS-C, that's a lot of reach. I bought my 300 F4L IS for $550 used from KEH.com with a warranty.
Feel free to look at my image gallery or flickr to see what kind of birding I get, as an amateur.
There are days I think to myself, "I really should have brought my 600mm today." But, then I think about it, and it's so infrequently that I don't really think it matters to me much. So I will eventually probably just sell my 600mm. As much as I want a long lens from time to time, I also don't want to deal with carrying it. The 150-600's are really nice in that they are light weight and small for what they are, so I keep mine around for that reason. Ideally I want a 400 F2.8 for my "big lens." I can always feed it TC's and get a 560 F4 or a 800 F5.6, and I'd rather have that speed for focus purposes. That's the rub with the 150-600, the aperture is f6.3 wide open at 600mm, so it's going to not have the best AF performance in poor light. F2.8 will focus better. When it comes to flight, I put all the emphasis on focus. So a shorter, faster lens is what I'd want.
Ideally, if I had a big budget, I'd want a 5DSR and a 500F4L (no need for IS for me on that one, it would be for in flight, otherwise, on a gimbal anyways). The 5DSR because the resolution lets you have the pixel density of an APS-C, but with a wide field of view thanks to being full frame, along with no AA filter, for more details. The lenses because they're of the best quality you can get and perform great with TC's (700 F5.6 being a great setup). But, heavy setup, big, bulky, and costly.
One thing for sure, I rarely need 70mm or 100mm when I'm birding or looking at wildlife. Personally, I always take a 2nd camera with a wide lens on it. My dedicated birding setup is a prime. I take a minor 2nd body with me with a wide lens for the moments I want to capture something huge or very close. I generally take my EOS-M + 22mm F2 as my sidekick (so small, light, compact, and wide and fast).
Again, it's all about what you do, how you do it, and what your experiences are. I went backwards from 600mm to 300mm to have a smaller, lighter, faster setup. But that's because I get so close now. I'm sure the moment I went to Washington in April to do Eagles, I'd be begging for a 500mm or 600mm and my 300 would sit in a bag, since you can't get near them across a river!