I have the 70-300L and use it almost exclusively for outdoor sports - football, soccer, cross country and track.
I use it with a 7D. My exeperience - AF is excellent, rarely misses, very sharp lens, IQ is great, the reach & range is perfect, and it is light enough to hand hold easily. For what I use it for, this "relatively" affordable lens is perfect.
I also have a 70-200 f/2.8 IS (M1). The AF can't keep up with the 70-300L - I stopped using it for outdoor sports in favor of the 70-300L, even with lower light situations (cloudy or dusk). I'd rather use a higher ISO and get in-focus shots than a lower ISO with a lot of misses.