I have a 6D and 7D. I've used both for middle school basketball games in a fairly dark gym in combination with a 70-200mm 2.8 II lens. The 7D AF helps me get more in-focus shots, but the 6D's better high ISO capability allows me to use faster shutter speeds and the in-focus shots have much better IQ with less noise than shots with the 7D and same lens. I get an in focus "hit" rate with the 6D in AI Servo mode of around 50% compared with around 70% for the 7D.
But, the greatly superior 6D IQ more than offsets the AF advantage of the 7D in my opinion. I'm only using the 6D for basketball at this point and leaving the 7D at home. If. You are shooting NBA games or athletes that move faster than 13-year-olds, you will probably have different results.
The 5D3 will of course give you great AF with excellent IQ. But, for me the 6D is a good enough indoor sports camera for the 5-10 times a year I'll use it for that. If you are doing a bunch of sports photography, get a 5D3, but if you are doing general photography including a limited amount of indoor sports, the 6D is a good option.