I went for the 70-300L for different reasons, but since the link to the crops were posted earlier we can play with them a little. The original poster has a crop sensor body, so we can disregard the full frame corners.
Roughly speaking, I see (70-200 f/4L vs 70-300L):
70mm f/4 on both: win for the 70-200 f/4 which is just sharper all round.
135mm f/4 vs f/4.5: possibly the 70-200 has a slight advantage in the middle, but both degrade away from that
200mm f/4 vs f/5: possibly the 70-200 has a slight advantage in the middle, but it holds on better in the corners
280mm vs 300mm f/5.6: too close for me to call in the middle, but the 70-300 has a slight edge going out where the 70-200 starts showing hints of CA.
From that you might conclude the 70-300's advantage is right at the long end, and if you your needs up to 200mm are critical, then the 70-200 can have a small advantage.
Personally, as wildlife was also mentioned in the 1st post, it's the 70-300 no question. You don't generally want to mess around fitting TC's in the field if you do find yourself needing to go from 70-280. Having the whole range in one go is much more convenient, and for general wildlife you will be finding yourself towards the long end a lot of the time!
While people tend to ask for "the best image quality" what then usually go for is "good enough" and other factors start becoming more important once that is reached. Outside of special applications the 70-300L is more than good enough.