I don't think the III has made it through the system to users yet. It's also about twice the price of the II.
The 2X mk II is a complete redesign compared to the mk I (and III is another complete redesign), in contrast to the 1.4X where I and II were optically the same with the II offering weather sealing and change to the internal light-absorbing material lining the barrel.
I have 2X II and still regard it as a somewhat expensive paperweight. I've tried it on my old 70-200 F4L and my 300 F4L IS. I used it with my old EOS 3 that would AF with it. I've done tests and tried using it in all sorts of combinations. My father has borrowed it and done tests with several lenses, particularly the 135 F2L. It has never offered any sort of decent performance for me. Whether things would be better with an F2.8 lens I don't know - people report decent results with the 300 f2.8L IS for example. Certainly I've not found any use for it with the lenses I have.
So in summary, yes the 2X II is different and reportedly better than the mk I. mk III is on its way and should hopefully be better than II which I've found disappointing.