I had the same choice and went for the 5D3. For me the decisive factor was AF, not for sports but for nature photography, where effective tracking with multiple AF points helps a lot. Another factor was interface similarity with 7D (earlier I'd found 60D UI very hard to get used to, and the 6D is similar) - and unlike some commentators, I've quite happily used 5D3 and 7D side-by-side, usually with wide-angle lens in the 5D3 and a tele in the 7D. Yes, 5D3 IQ is better, but in good light 7D is qood enough for me - and in focal-length limited situations with long lenses the crop factor helps.
So: If you've used and like the multi-point AF modes of 7D for tracking moving objects, you'll be be better off with the 5D3. If you can get along with center-point AF only and don't care about differences in ergonomics, go with the 6D.