Let me ask the group...I own a 70-200 f/2.8 IS Mk II. Would I see enough of a difference with the 135 @f/2 to make it worth buying a nice used one?
I have had both and kept the 135mm L. Not because of IQ so much as weight and that slightly larger aperture does help, since I find myself needing all the light I can get.
The 70-200 is absolutely supurb while the 135 is more of a speciality lens. I really would not recommend that you switch, and I doubt that you would gain anything unless you shoot in very dark areas with moving subjects, for stills, the IS will get you there and then some.
My 135mmL is not going away anytime soon!