I am upgrading to a 5d mkiii and I shoot sports both indoor and out. I realize ten shots per second is much better than 6, but outside of that, I am guessing its performance is close to being on par with the 1dx. or am I wishful thinking.
Not wishful thinking at all - I used the 5d3 all last spring and was generally happy with its' performance (c/w the 7d I used the past 2 yrs). I did use concurrently with the 1d IV last yr, with different lenses on each to add to my flexibility / readiness. With knowledge of the game, nailing focus on a serve, dig, or block was rarely a problem for the camera. Planning the background (when possible) and controlling DOF is more 'operator-dependent'.
While I clearly prefer my 1-series now, I'd easily be able shoot all day with my 5d3 and my client's would probably not notice much difference. But as for all the conveniences / customization / durability of the 1-series, shooting matches 2-3x/wk is more pleasant (? reliable) over the long season.