You: I'm debating whether I should get the 200mm f2 or 300mm f2.8. My budget is $6000usd. I want a lens I can use for sports and theater. I already have the 70-200 f2.8. Which would be more ideal for my use?
For years I've said that the 300mm f2.8 is the one "Must Have" lens, but I have to admit, I bought the 200mm f2 last year, and it's my new favorite. I take it with me to every assignment (Not just the sports stuff). It's amazingly easy to hand-hold, and it gives you the look and feel of a 300 while being able to shoot much closer to your subject.
You're dilemma is a tough call. It really depends of the types of sports you typically shoot. For most "Theater" type stuff and indoor sports, (Basketball, wrestling, gymnastics...) the 200 works great. (And being a stop faster than the 2.8 is a huge plus.) But if you shoot a lot of outdoor sports, (Football, baseball, soccer...) you'll find the 200 just doesn't have enough reach.
Which ever lens you decide on, I would highly recommend getting a AF-S Teleconverter TC-14E II. (It would convert the 200 into a 280mm f2.8, or the 300 into a 420mm F4, and it's still tack sharp.)
One last bit of advice...If you do get one of these lenses, always shoot it wide open, even you you have a ton of light. With these kind of lenses, if the focus isn't perfect, being at f5.6 or f8 isn't going to help you, and it will only ruin the beautiful "Bokeh" these lenses are famous for.
Hope this helps.