When you shoot tele you deal with a lot of the "transition zone" that can make for some ugly bokeh. The 70-300L does a nice job with that transition zone. I have not really seen anything too ugly coming out of it. Having owned two copies each of the 70-200L (IS and non IS) f/4 zooms, I can safely say that I prefer this lens to those. I haven't used Canon's 70-200 f/2.8L zooms enough to have an opinion there, but the size of those lens makes them less of a travel option. I would probably love the 70-200LII for my event work, though.
Indeed, quality of the bokeh in stark gradient areas is a real differentiator and this doesn't always show up in "measurements". In this context, the 70-300L generates really plesant bokeh.
As for 70-200's, I own the f/4 IS and the f/2.8 IS II... While the 70-200 2.8II is a highly competent sharp zoom, it is not the second coming as some fanboys would have us all believe. It is sharp and versatile, but also heavy, and obvious. And most fair-minded people will agree the f/2.8II is not known for its silky bokeh... then again that may not be its main purpose. I periodically knock the 70-200 2.8II here simply because some fanboys just praise it to the heavens... I jokingly call it the "I-too-have-arrived-pricey-but-achievable-newbie zoom", just to poke them a bit .
Here is a 700-200 f.2.8 II image and the bokeh crop...it is competent zoom even on grey winter days but I never found the bokeh something to write home about.