SO the 70-200 f2,8 IS L gives better results, even with a 2x convertor? Better than a 400mm L non is or 100-400mm L IS? Ofcourse for the price of the 70-200mm 2,8 with convertor, one can buy two good lenses; 70-300 IS L + 400 5,6 L.. G.
Unfortunately Canon has ignored that focal length (and price, size and weight) range. Both 100-400 and 400/5.6L are very old and would benefit from upgrade (but not so for our wallets ...)
Some will autofocus only wide open at f/5.6.