So looking at your tests, it's bizarre that the EF 2x III is better, but Bryan's crops show the RF 2X having a clear advantage.

My only explanation is the RF extender is optimized for the RF 600mm. Which if I am correct is optically the same as the III. And since you were testing it on the EF 600mm f/4 II. Maybe that is the reason for the discrepancy between your results and Bryan's results.

But even then it hardly makes a lot of sense since the 600mm II is actually a touch sharper than the 600mm III.

There possibly could be some sample variation in the mix as well.