I upgraded from Mk I to Mk II. There are 3 things that I consider its worth the upgrade and IQ is not one of them since both lenses produce stunning pics and I could hardly see the difference.
1) The most important thing for me is weight reduction since I like to shoot hand held and always carry it when I'm hiking.
2) 4 stop IS. I like to go inside the forest when I'm hiking so instead of boosting the ISO I can reduce the shutter speed and get good results.
3) IS mode 3. I kinda like this feature, and almost always use this mode especially for birding.
I have used 1.4X & 2X TCs mk 2 for my 300mm mk1 and to be honest with 1.4X it still focused quite fast and IQ was good, but with 2X both speed and IQ were degraded significantly.
I only tried 1.4X mk2 with 300mm mk2 never with 2X TC. With 1.4TC mk 2, my 300mm mk2 performed better than mk1.
I think with 300mm MK2 you should use TC MK III, I heard both 1.4X & 2X TCs MK III perform very well with new version of telephoto lenses