The problem with any of the long consumer grade zoom lenses is they are slow at the far end. The 55-300 is ƒ5.8 @300mm. Inside in a poorly lit school gym, not likely to get much unless you crank the ISO way up. Then you are fighting noise (grain) in your image.
You should try shooting in the gym with your 50-200 before you invest in another, if you can get the quality you are looking for with the 200 @ ƒ5.6, you will be happy with the 300 @ƒ5.8
A ƒ2.8 (constant) zoom at 200mm and crop to 300 would likely do better than the 55-300, but more $s.
The 55-300 also hunts focus in low light, takes some getting used to. I regularly have to manually rack it back out to infinity before starting to aim and focus again. When it missies it comes all the way back to closest focus. Annoying and time consuming. I do like it for outside work in good light though. It's a good, compact lens that performs above it's price range.
Last edited by K-Three; 12-13-2015 at 02:22 PM.