I have both cameras. While the AF on the 5D3 seems to be better in most circumstances, particularly low light where the Mk4 can struggle, in most circumstances I'd regard the Mk4 as the primary sports body. It has the massive advantage of 10 FPS and a deep, deep buffer. It never ceases to amaze me how much actually happens between frames when shooting fast moving action at 10 FPS. For peak sports action 6 FPS feels almost glacial by comparison. Using the 5D3 for sports will deliver you satisfactory results, but may require a far higher degree of anticipating the "moment". And if you shoot on "continuous" a lot, it's reassuring to have a shutter rated to 300,000. But these numbers are very conservative. There are plenty of 1-Series bodies way over 1,000,000 actuations on their original shutter. I ran a 5D classic up over 250,000 on the original shutter.
Then there is the issue that doesn't seem to concern some photographers in the slightest, and that's the 5D3 black focus points. The fact that it isn't an issue for all photographers does not make it a non-issue. Otherwise there would not be so much broad based discussion on the subject. It's irritating and can cost you money to miss shots because you've lost track of your focus point in situations where you would have got the shot on the Mk4 with the illuminated, red, visible AF point.
Thirdly, the Mk4 probably has superior weatherproofing. But for me the biggest 1D4 advantage lies with the unrivalled 1-Series ergonomics. They are just so fantastic to use and handle, they are a very evolved and polished design. Everything just falls to hand so perfectly in obvious and subtle ways which the bulky 5D3/BG-E11 can't quite match.