With static subjects, I use One Shot. With my 5DII, I almost always use One Shot because of the disappointing results I get with AI Servo, regardless of lens. On my 7D, if there's movement or expected movement, I use AI Servo. Shooting with my 85mm f/1.2L II on the 7D in AI Servo, several times with young daughter running diagonally toward me, I got about 8 of 10 shots in crisp, eyelash-counting focus despite the 'ponderous' AF of the 85L.
I haven't used the 5DIII, but given that it bests the 7D on AF, I'd not hesitate to use AI Servo with fast primes wide open - I certainly will be doing a lot of that when my 5DII replacement - a 1D X - arrives.
what focus mode ddo you use? zone? spot? i havent had such great results using spot and trying to maintain tracking of a persons eye walking towards me
On a 5D Mark III, it is a completely different ballgame than on a 1D body, such as the 1D Mark IV. Since metering is always done through the center point regardless of chosen AF point, I use center-weighted average metering. I set in Av mode, decide my aperture, which is usually 6.3 for indoor sports, set my shutter speed to 1/500, then set ISO to auto. I shoot a few shots in real life situation then read the ISO reading. Switch to Manual and program that ISO setting in. If I begin missing, I set ISO back to A and maybe do an EC of +1/3 or +2/3 or simply raise or lower my ISO value with the click of button and the thumb-roll of a dial. On the 1D 4 this isn't necessary, you can set it to Av, min shutter speed, and auto ISO. 5D Mark III takes a bit more work, but it can be done.