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Depending on what your expectations are, there definitely some "off brands" for consideration.
In my quest for "long glass", I went with my Sigma 100-300/4, but also looked at the Tamron 200-500. The focus speed on the Tammy was pretty slow by comparison to the Canon 400/5.6. My Sigma is pretty quick if you aren't asking it to travel from one end to the other. My experience with the Canon 70-300 wasn't the IQ that was a turn-off, but the focus speed that was so slow. I find the Sigma 100-300/4 to be a good blend of speed/IQ/$$. It played nice with its matching 1.4X, but the 2.0X just got to be too soft.
But, if you are wanting focus speed, the long Canon's (100-400, 400/5.6, etc.) are kinda tough to beat, especially on a 1 Series body.
I haven't done much "birding" since I was down in Trinidad, where 300mm was plenty due to the proximity you could approach many species. My current super-tele is the Vivitar 120-600 (manual focus).
Roger (of www.lensrentals.com) brings out a point about long zooms ... you typically wind up shooting them at the long end anyway. From that, the Canon 400/5.6 would be my choice over most others that I'm aware of. Quick, light, great IQ, reasonable $$$ ... holds its value and performs well. Until you need to make the jump to the BIG BOYS that you can't hand-hold, I don't know of anything that trumps the 400/5.6 for reach, IQ and practicality at a $$ for mere mortals. I'm holding out for the 400/5.6 II with IS, wishing for either a 350/3.5 or 400/4.5 but those aren't gonna happen.
Some people use the 300/4 IS with a 1.4X ... which gives you a 420/5.6 with IS. I'm a bit torn between this setup vs. the 400/5.6. Fortunately, long glass isn't my current forte, so I can wait to see if someone will bring out a different solution. BTW, the Sigma 120-300/2.8 OS is worthy, but the $$$ and weight change things a bit.