Nothing, they work as two seperate controls.
If i really give it beans out of a corner the ATB pulls the power to the wheel with the most grip, but theres a limit to a tyres ability to hold that grip to put the power down, the moment that the tyre stops gripping and starts spinning up the ESP cuts in and stops that.. although its not as clean cut as that, its work along the lines of that..
The basic was, before the ATB diff, the ESP and TCS lights used to bling every odd sec on corners with a little bit of speed, since the ATB diff, i hardly get either lights, the main time i see the ESP light come on is on a damp morning and i give it to much power on a roundabout, and the diff puts to power to the best grip but still spins up, hence esp cuts in..
I rarely turn the esp off, as its a safe guard if the ATB doesnt do what its predicted. I have turned it off on the occasion, but found when throwing the car into roundabouts without ESP, the car is abit aggressive on the tyres and as i dont intend replacing low profile 19" every odd month, i tend not to do that alot! lol