Limited slip differentials attempt to keep wheel SPEED EQUAL. They don't, of course-you have to go around turns. Open differentials keep wheel TORQUE equal. This may not make sense at first when you consider one tire spinning, so lemme explain it this way...
Let's say you have one tire on ice, and the other on pavement. The car has to go uphill, and the differential is an open style. You're not going anywhere, because the tire on ice is gonna spin. The tire on pavement is actually trying to move the car forward, but it only applies as much forward torque as the other tire is absorbing as it spins. Wanna quick way to get out? Apply the parking brake moderately. What happens is, the brake will exert a fairly large drag on the spinning tire. The brake will also be applied to the stationary tire (the one on pavement), but since that tire is not already spinning, it's not having to overcome as much friction as the spinning tire does. This means that the torque applied along each axleshaft remains equal, but one side is using more of that torque to overcome brake friction, since the other side is not spinning. So, the non-spinning tire has more torque left over after brake drag to start moving the car. Make sense now?