The 70-200mm F/4 IS is a very nice lens (one of my all time favorites), but mine did not work well with a 1.4x TC, so 200mm was the limiting factor. The 100-400L is also a nice lens, but it's optical quality cannot match either the 70-200 f/4 or the 70-300L. I found that upscaling images from my 70-300L @ 300mm to 400mm were almost as good as my 100-400L @ 400mm. My 100-400L was always soft between 350-400, but the 70-300L is sharp throughout. The 70-300L is easier to carry than the 100-400, yet just as sharp as my 70-200 was. Focus speed and build quality was excellent foe all three.
With the 100-400 limited by merely good IQ, and the 70-200 being too short, the 70-300L has become my favorite zoom. My 70-300 has now replaced both of these lenses, meaning I can now carry one medium-big zoom instead of two.
If I could only own two lenses on my crop 7D, the 70-300L would be one and the other would be the 17-55 F/2.8 IS. For my old FF 5D I would have chosen the 70-300L and 24-70 F/2.8. My 70-200 F/4 IS would be next choice, if I had never owned the 70-300L. I never really grew to love the 100-400, although it was pretty competent.