My telephoto zooms have progressed from 55-250, to 70-200 f4 IS (w/ 1.4X extender), to 70-300L, to the legendary 70-200 f2.8 IS II. I still have all three L lenses. And the one I grab when I need a long lens is the 70-300L.
The 70-200 f4 IS is sharp on its own, but degrades with the 1.4X on it. The 70-200 f2.8 IS II is so heavy it is literally a pain for me to carry; and it comes up short focal-length wise now that I've gone full frame; and at f2.8 the depth of field is so thin I can't get things in focus unless I stop down to f5.6 or so.
The 70-300L gives me extra reach, gives me photos that look as good as the 2.8 delivers, gets both eyes of a meerkat in focus wide-open, and I don't have to ice my elbow after an afternoon at the zoo. To boot, while thicker than the 70-200 f4, it is shorter and fits in my holster-type bag with enough room left over for a small flash.
So, if I were going on a photo-opportunity-rich trip where I had to carry all my gear, I'd go with my 5D3, the 24-105, and the 70-300L.