The 70-300L conclusion is mixed? That is news to me. I've only heard praise for the lens. The only negative I have heard people complain about is the variable aperture (f4-5.6) and that it is "slow" compared to some of the other lenses.

I own and use the 100-400L for almost exactly what you describe. But as soon as you decide to spend ~>$1,000, Canon has several excellent telephoto lenses. So, selecting which is best for you becomes pretty specific and could vary depending on if you shoot a crop sensor camera or FF. But, a quick guide based on what I have read:
  • 70-300L: Excellent sharpness, fast focusing, 4 stop IS, latest technology, and weather sealed. Focal length range is good for general purpose telephoto. Aperture is a little slow, so you need good light, especially at the longer ranges. Light, and fairly compact.
  • 100-400L: Longest telephoto zoom for under $2k, 2-stop IS, old design, good sharpness. Great focal length range that pairs well with most general purpose zooms to cover a wide range with two lenses. "Slow" aperture, so you'll need light.

Canon has 4 "L" lenses in the 70-200mm range. This is a great range on FF. I shoot a crop sensor camera (7D) and while I am tempted by the faster aperture and sharpness of these zooms, it hasn't been enough yet for me to pull the trigger as I just don't shoot that range all that often.
  • 70-200 f/2.8 IS II: Generally regarded as the best zoom canon makes. But it is expensive. Can be mated with a 1.4x or 2x extender to make it a 105-280 f/4 or 140-400 f/5.6 lens (AF speed decreases with adapters).
  • 70-200 f/4 IS: Excellent sharpness, many on the forum love this lens.
  • 70-200 f/2.8 non-IS: Older lens, still great IQ, no IS.
  • 70-200 f/4 non-IS: Older lens, typically the most affordable, ~$650. Still very good IQ, no IS

Then you also have primes, which tend to be sharper than zooms, such as the 300 f/4 IS, 400 f/5.6 non-IS. So, it gets down to what you want and what you'll use.

I am very happy with my 100-400L. I probably use it about half the time. I did buy it before the 70-300L came out. But I don't think I could give up the reach I get with 400 mm.

Hope that helps, good luck,
Brant