It depends on what you mean by “photographing birds.” (Seriously.) Bald eagles circling above? Great blue herons in nests? Plovers on the ground? Hummingbirds on a feeder? Ducks in flight? All these scenarios are quite different. And what do you want to take? Just the bird up close or in geographic context? A zoom lens allow flexibility for moving objects (birds) and also it is somewhat easier to find the subject in the viewfinder and then use the auto-focus (animals/eyes) to “lock on” at 100mm than 400mm; usually you start wide and zoom in. I used the EF100-400 ƒ5.6 in Kenya on a recent safari trip perhaps 80% of the time, and was constantly zooming in and out, depending on the movement of the animals (lots of birds.) Ultimately I came home and traded up to a RF100-500, because the 400 just wasn’t “enough.” I have the 600mm ƒ11 which I like a lot (and also brought with) - and do not find the fixed aperture particularly limiting except on dark days. What I do find limiting, however, is the fact that objects you are tracking can get “too close” and then, as a fixed focal length lens, you are stuck and then can't get “far enough away.” But it’s very light weight, fast focusing, and you can get really close. I found the fixed 600mm length very limiting to use on a safari as the distances and size of the subject (Birds? Elephants? Giraffes?) varied so much.
RE: your blurry shots, keep in mind the SS-Focal Length of the lens rule of thumb that your SS should always be 1.5 - 2x the focal length of the lens, e.g., using a 500mm lens you should be shooting at 1/1000th to be safe.
RE: Tele-extender: controversial as there are photographers who say “no problem” and others who say “only as a last resort for special occasions…” Frankly, I’m more in the latter. It adds a lot of bulk and length, which adds clumsiness to your motion, and it certainly doesn’t make your photos any sharper, especially on a non-“L” lens. Besides those things, with tax, are $550 -$650! Why not just put the money to a better/longer lens?
Anyway, it depends on what you are mainly going after. There are times you’ll need to “back up” and there are times you wish you could get closer. My only advice is go for the longer telephoto range. I would recommend getting the RF100-500 lens. No one ever complained that “I have too much zoom.”😉 Good luck!
(First three images all taken at 400mm, uncropped. But these are all large birds. The 4th image, the yellow-billed Hornbill, a much smaller bird, was also taken at 400mm but cropped. All of these are taken at around 8-10m, if memory serves...)
