6D, plain and simple. The 7D has no advantage what so ever for your needs over your current 600D (T3i), as they're the same sensor and same ISO ability, etc. The 7D just has better autofocus, but everything else image quality wise, they're equal basically. The 6D on the other hand has quite a jump in ISO performance and range, better dynamic range, higher resolution, and a much more controllable depth of field per focal length, being full frame instead of APS-C, which is nicer for portrait so that you can have better selection of lens per focal length.
Now, the 6D is not ideal for sports. It will do fine, if you simply learn to shoot action. I can shoot kids soccer no problem with a T4i which is essentially the same as the T3i for the most part. FPS doesn't really matter to me, as long as it's 3~4 FPS it's more than enough, I don't just spray 6~7 FPS when shooting, as I don't want to sift through 1000+ photos from an afternoon, looking that one shot.
Really I would just suggest you practice more with your T3i for sports and keep it for that. Outdoor sports, with ISO 800~1600, and develop your post processing (noise reduction) work flow so that this isn't an issue. Granted, the 6D can do just as good, if not better (especially for ISO pushing to keep high frame rates) if you practice it too. Both cameras lack high FPS. The only advantage the 7D offers you here is higher FPS and a better autofocus system for action. The question becomes... are you willing to sacrifice quality everywhere, just for high FPS and AF?
This is where the 5D3 comes in. Or a 1D series. But it depends on your budget, if you want to get the best of both worlds.