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Originally Posted by jeftrz
DTC's function is similar, however instead of a mechanical system in the differential the car's computer applies the brakes to the slipping tire to stop the slip. This increases the torque required to spin that tire, and hopefully transfers the torque back to the non-slipping tire.
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Excellent explanation. I just wanted to add that Wikipedia tells me that if DTC is braking a spinning tire, torque transfer to the other tire should not be "hopeful" but automatic. Having DTC apply the brakes to a spinning wheel (for example, on rear wheel on ice) raises the reaction torque at that wheel, so the differential compensates by transmitting more torque automatically to the other wheel.
Based on my limited understanding of how this stuff works, an LSD is extremely beneficial when exiting corners while stomping on the gas. DTC is extremely beneficial when losing traction due to road conditions. But neither does the other's job nearly as well.