I think you're underestimating how sharp the 70-200 IS II is. Take a look.
I have the 70-200 IS II, 85L II and 135L and in real life shooting, the 85L II and 135L are way more sharp compared to my 70-200 IS II and it's not a bad copy, I could compare with half a dozen similar zoom.
The test shot like the one you show me are nothing like real life shooting
Take by exemple the 24L II, it looks incredibly sharp on the test on that site, but in real life, almost 30% of the pictures are out of focus, so it make that lens useless in some situation
Always keep in mind that you won't be shooting number and line when you will be in studio doing fashion or outside doing landscape or street photo
Look also at the 50 1.2L on that website, It looks awful but go find some real pictures in real life situation taken with the same lens and you will see it can be crazy sharp
Black on white test shot are really killing some good lens, they look awful on such test but in real life situation they look awesome
It's all about personal preference, both can be good, it all depend of your shooting style, but I will never use my 70-200 in the studio if I have my 85 or 135. I will use the 70-200 if I'm outside doing sport or something that is too fast for me to change lens between shot.
And keep in mind something, 30 years ago some amazing photographer were able to take amazing pictures that many of us will never be able to make, and they did with lens that look completely awful on these test chart
And if you think it's all about that kind of test, I know people here hate DXO but what about this :
2 different site, 2 different result, 2 different stories
I don't want to bash what you said, but have you ever tried all 3 lenses before or you just tell your conclusion by looking at some test shot on that website?
If you buy a lens just by looking at that website, you got it all wrong my friend
Rent the lens and zoom, go shooting for a day or a weekend and choose what's best for you
In my case, I don't need a zoom for what I do, I need sharpness, and for my own personal taste I really believe the 85L II and 135L are a lot sharper then the 70-200 IS II
But in the end it's all a matter or personal preference... I just wish you tried all 3 lenses before commenting on their performance, have you tried all 3 ?
I have had each of these lenses. I no longer own the 135L or 85L. I was never disappointed in the 135, ever. The 85 when it hit it hit with impact. The 70-200L II never fails me either and there isnt much real world change to the impact of my images compared to the 85 and 135 other than larger apertures but at 200mm the dof is extremely shallow. the 70-200LII F2.8 at 135mm .3ft, at 10ft F2.8 is .1 ft dof. The 85L 10ft F2.8 is .7ft dof, even at F1.4 it is still .3ft in focus. So if blurred effects are what you are after the 70-200 is no slouch, however the bokeh of the 85L is legendary. The CA on the 85L is really bad in some situations. The 70-200LII flare and CA are pretty much close to eliminated. For me the 50L takes care of my 85L lust and the 70-200 takes care of my need for 85 focal length. Not sure why 85mm it isn't a marking on the 70-200LII, i have considered locating the 85mm spot on the lens and marking it myself. Sharpness is nothing left to be desired on the 70-200L II either. Can't say why you don't talk it up more than you do. I shoot Primes as my primary but the 70-200 is a cut above any zoom and if the next 24-70 is anywhere similar it will bang out wedding images to perfection. The benefit of the newer model will be the metal bearings inside the lens zoom portion. When those wear out as mine have the zoom doesn't lock focus correctly. They replaced this in my lens as well as the zoom barrel and it was back to one of my most reliable lenses. Honestly though the 70-200 never fails me whereas my primes often do. Can't brag louder about that kind of performance!