I just received a new to me 1d mark III after not being very happy with the 7d. I can definitively say that the 1d mark III is more flexible and has more consistent focusing. One major thing that really frustrated me on the 7d was when I put it on af priority mode (custom function) the fps would drop dramatically from 8 to as low as 3fps in many cases. On the 1d mark III it will maybe jump down from 10 to 8-9. This can be very crucial in getting the shot or not getting it. Also I have less out of focus shots with the 1d mark III imho today from shooting a tennis tournament and a baseball game.
So long 7d