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Sometimes it is not easy to understand what is going on with those darn extenders, and what kind of variations one might encounter from one application to another......all I know is that my 300 f/2.8 IS MkI works better with MkIII 1.4xTC and 2xTC, than with the MkIIs ( I am referring to IQ only.)
Also, I have been quite impressed with the MkIII TCs on 70-200 f/2.8 IS MkII as far as IQ is concerned, although I never tried that lens with the MkII extenders.
Lastly, I have found that 1.4xTC MkIII works fairly well with 800L and 500 f/4 MkI, again, talking about IQ.
In all of the above instances, I haven't seen any differences in AF performance between MkII and MkIII extenders.
I believe canon white papers still states a 75% decrease in autofocus speed with Mk II and Mk III 2x extenders, though it may hunt less/focus more accurately. So I am not surprised.