I own both the 135f2L and 200f2.8L II and have also tested them extensively with Imatest. Both of them belong to the sharpest of my lenses, with great contrast as well. Even the 135f2L + 1.4x combination works great - but so does the 200+1.4x, too.
Regarding sharpness, contrast or AF speed, there is really no significant difference between these lenses. Both of them leave the zooms in the dust.
I would say that the decision should be based on your focal length and optical speed (widest aperture) requirements. You can easily crop an 135 image to a 200 frame with relatively little loss of resolution - but not the other way around. Also, indoors you seem to always be lacking light. If I were you, I'd choose the 135mm for the purpose.
Being me, however, I seem to use the 200 more, though, with a crop camera.
My apologies for not keeping my profile up to date. There have been some changes there which would have made things clearer. Sorry, but I updated it now. So, the idea of selling the 70-200 4.0 IS is a good one, but would not buy the 70-200 2.8 again. Too big and to much $$$. When I said that money wasnt the driver here, I meant between the 135 and the 200, which is only about $300. But money is a big factor overall. So the sale of the 70-200 4.o IS would fund the 135 purchase. I appreciate all the responses from everyone, and the great examples of stage images. If I had to, I can rent the lens I need for a gig, so thats an option. Other than that, I think saving for a 135 2.0 is the way to go and add the converter since I already own that.
I'll simply add that you would not shoot at 200mm unless you had to. It's better to be closer. So if you know you need 200 that's what you need. But you wouldn't want to be back further simply because you had a longer lens.
But sometime with a tall, formal stage you have to be back to not shoot too much up at the performers.
You don't want it, but if I HAD TO shoot performers with only one lens, it would be the 70-200 2.8 IS.