300 f/2.8L IS II is awesome. Sharpest lens in Canon's line-up and killer bokeh.
Any extender on the 200mm f/2L IS and it falls to pieces.
Well I can agree with the first point, the 300f/2.8 II is an amazingly sharp Lens & it does work well with the 1.4x III Extender, the 2x III Extender not as well, but that's to be expected.
I can't see the 2nd point though, the 200f/2 works just as well with the 1.4x III Extender as the 300 in my experience, perhaps not as well as the 300 with the 2x III Extender.
I've had the 200f/2 for several Years now & used the Lens extensively, my current 300f/2.8 is the Version II, bought after selling the Version 1, both these Lenses are sharp, the V II maybe, maybe a tad sharper, but the benefits here at least to me have been mostly in the weight distribution and the weight loss.