Only in someone's dreams do those two lenses compare in image quality for a full frame camera. The 70-300L is an EF lens but is positioned more as a step up for crop camera users.
I already know how good the 70-200 f/2.8L IS II and the 300 f/2.8L IS are. That's what I am currently using. Their performance is stellar. I also know that the focal length range I need is 70mm - 300mm. It would be nice to have it in a single lens. The 100-400 just won't do it for me.
Even if beating a dead horse: please be aware that comparing the 70-300L to the 70-200L+extender (ie. if you also want the 200-300 range) is like comparing it to the 70-300 non-L: It's a completely different class of lens, and that's why they don't cost the same! The white color and red ring seems to fool people to put them in the same category as 2.8 tele prime or zoom lenses, but the said lineup is just as JoeDavid said. If you want to compare it to anything, it's the 100-400L which is in the same price range.
Concerning iq: Looking at my 50k pictures I shot last year, I have to say corner sharpness seldom matters for me. Even if cropping nature pictures to a "golden cut" the sharp zone is mostly not in one of the corners, but the bokeh or "sharp noise" like grass is. And furthermore I'm using a crop body, and the sharpness falloff is only visible on full frame.
At the same time, for my ease of mind I am quite happy if carrying around not 5000€, but 2000€ when crawling through the woods - less gear that can be stolen, dropped in the river or overrun by a truck ... L build quality and weather sealing don't help in these cases, and this is a thing that's seldom thought of :-p
Personally, I'd be happier if the 70-300L was not white and had a black ring, it's the *price-iq-weight-length-zoomfactor-is-af* combination and tradeoff that makes it attractive. And as proven here, you can pretty good shots out of it.
