I did not find much difference of the 2x II versus III on my older lenses.
First of all, the IQ with the 2X is not great. Good, and it serves a purpose, but not great. I prefer using the 1.4X and cropping. I believe this provides superior IQ to the 2X.
I had hopes the 2X III would be an noticeable improvement on my older 70-200mm f/2.8L IS, 300mm f/2.8L IS, and 500mm f/4L IS - all the original, no Mk II.
Sadly, the 2X converters see almost no use for me. I suggest you get the 1.4X III and crop when needed.