I'd go for the 70-200 2.8 (non is). I don't think f/4 will do well for stage shots, unless the stage is incredibily well lit, which sadly is a bit of a pipe dream for photographers. Just make sure you shoot in RAW, and whatever lens you get you'll be able fix those pesky skin tones you get from the dodgy lighting.
I forgot to add they have broadcast quality lighting and that is a big reason I'd consider the f/4. I do shoot raw and the last time I shot in that room I didn't have to mess with skin tones, they were pretty much right on with just the in camera white balance detection.