LSD is mechanical and traction control is electronic.
An LSD is inside your diff. On a regular diff or open diff, power goes to the wheel with the least grip and often your inside wheel will spin. An LSD sends the power to the wheel with the most grip hence reducing wheelspin.
Traction control is in your ECU using sensors it can tell that a wheel is beginning to spin and will momanterily back off your throttle until the wheelspin is eliminated.
Theres pro's and cons to both. For pure driving performance its LSD all the way. However an LSD can cause severe torque steer in a Front wheel drive car, aswell as make a Rear wheel drive car twitchy and unpredictable at low speeds. The main con with Traction control is that it saps power, but it can often be switched off.
Hope that explains it