It is not much surprising that that both wide open are similar...There is no way 70-200 II at email@example.com = IQ of firstname.lastname@example.org.
I own both (+85/1.4, 200/2) and all those primes render better contrast and sharpness across the frame...
Actually, the 135mm f2 @f2 (wide open) carries simular sharpness, contrast and colour to the 70-200mm f2.8 L IS II when shot in the 135-200mm @ f2.8. It's surprising but true. The prime flares more but has slightly less fussy bokeh wide open, but the 135L when stopped down to f2.8 the 135L renders worse. The non rounded aperture blades are pretty obvious where as the zoom stopped down a stop or two looks nicer.
It's easy to split hairs when trying to see which is sharper. For my lenses, there is little difference between them. Yours might be different.
But I need to use F3.5 - 4 on 70-200 II to get the same IQ as 135 @ 2.8. (BTW: The same apply to the 300/2.8 IS I.)
Problem with flare + yellow cast on 135 I have only in direct sun light in the frame or near the frame.
Bokeh: it is hard to tell, but I did not notice any problem with 135/2.8+ vs 70-200/3.5+