The main advantage is you can use other AF Points other than center on the 5d III... Haven't noticed a difference in focusing speed. I love my 85L II for portraits and have rarely missed a shot and isn't really an issue. For sports, I'll grab another lens. Let us know your experience once you've rented it!
Canon 5DIII, 5DII, 24mm TS-E II L, Sigma 35mm ƒ1.4, 50mm ƒ1.4, 85mm ƒ1.2 L II, 100mm ƒ2.8 micro, 200mm ƒ2.0 L IS, 16-35 ƒ2.8 L II, 24-70 ƒ2.8 L II, 24-105m ƒ4, 70-200 ƒ2.8 L II, 3x 580exII