And in many gyms, you are going to need to shoot at 2.8 and high ISO to get a high enough shutter speed to stop movement. In those situations, you won't really be able to stop down to improve the sharpness. I've shot with the more recent Tamron and I'm sure both are excellent lenses but they are not as quick to focus as the Nikon versions, but they are quite a bit less expensive...
Your choice in lens really depends on where you are shooting from and the images you are trying to achieve. I've gotten some excellent images sitting at the edge of the floor with a 24-70 (also f2.8) and some nice "whole team" shots with it further away. I've shot cheer competitions with everything from the 24-70 through my 200-400 (top of gym shots). There is really no need to consider the longer lens 99%+ of the time but I had it available and used it for some special shots I wanted to get. It normally stays home for indoor events although it becomes my primary lens for outdoor sports.
If outdoor for football games, the 70-200 will work well from the stands and the 24-70 is excellent again when you are up close.