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I have tried the two combinations.
the 70-200 2.8 IS II with 2xIII is about creates images which are about 10% more magnified than 100-400. is has a slightly narrower fov, so the 400 is more like 380.
the combo is a little heavier, and I find does not balance as well as 100-400. Of course the IS is much better on the combo.
for me, center sharpness is actually very close, with only a slight edge to 100-400 at f 5.6 in center. the corners more edge to 100-400. on 5d3, I find both of them good at f 5.6. On 7D, the difference is a little more visible.
Initial focus acquisition is very similar in good light. Tracking is superior on the 100-400 for BIF, when bird is moving towards you. the 70-200 with tc struggles there. of course the 100-400 is not fantastic either.
I would say, on the full frame, for non BIF use, if you dont the slight increase in weight and front heavy ballance of 70-200+2xTC, it is quite an adequate substitute for the 100-400, and in fact in certain cases, (shooting handheld at anything slower than 1/640 sec) will improve your keeper rate and general sharpness b/c of much better IS.