True LSDs provide lockup on both acceleration AND deceleration, irrespective if both wheels have traction or not. TBDs prove lockup on a progressive basis on acceleration only, and only if both wheels have at least some traction.
If you put a car on a hill, with, let's say the right side of the car on ice, and the left side of the car on nice, warm, grippy, heated pavement and try to climb the hill, the car with the LSD will go up it just fine. The car with the
TBD will not move.
The lockup of an LSD on decel is helpful in stabilizing the car while braking into a fast corner, but the real advantage of the LSD is that if the car lifts a drive wheel while cornering, it will not lose power delivery. LSDs can also be tuned to determine the amount of lockup that will occur, on both accel and decel. TBDs just can't offer this.
The downside to an LSD is that you get lockup when you sometimes don't want it. This can cause understeer in slow, tight corners (this is why autocross guys prefer TBDs). Also, LSDs will require more maintenance than a
TBD, since the clutch packs do wear.
Generally speaking, for street or autocross applications, the
TBD is the better choice. For a track car, esp a higher powered one, the LSD is the winner. For most of us here, the
TBD is the better option. The only thing to think about is that for those that do drive their cars in the winter, the LSD will provide much better traction due to the reasons mentioned above.
Hope that helps.