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I have the 70-200 2.8 and the 2X converter. The new version of both. I am happy with what I get both with and without the converter. Is the 80-400 better. I have no Idea as I have never used one.
Interesting One_oh_Four. I have used the latest TC1.7 on the older 70-200 F2.8 and the results have been excellent. I have had no issues with sharpness at 2.8 or 4 or 5.6. Most of the time I am shooting between F7 to F11.