Basically :
The "plate" style LSD uses friction plates or clutches inside it that under load basically end up locking together gradually,but always putting power to both wheels at the same time.
You can set the "slip to grip" ratio by the amount of preload on the diff.
Advantages? Have some sort of friction even under off throttle conditions, so they are very good for high speed racing, say turn one at Eastern Creek.
Disadvantages? more of an opportunity to understeer in low speed corners, but you can tune it out with some work!
Here's an exploded view of a ZF unit.
http://www.alfabb.com/bb/forums/showthread.php?postid=33954#poststop
The "Torsen' style LSD uses a series of gears inside it to provide the lock up. The difference here is, because the way the gears mesh against the drive axles, it can feel which of the two wheels has the most grip and therefore the power is directed to that wheel.
Advantages? The difference here is that under normal driving conditions and off throttle situations, the diff acts like a non-LSD diff, making cornering easier.
Disadvantages? Only thing I could think of is if you backed off at high speed (say 160kmh) into a corner and you had no form of friction braking other than the engine, it might snap out at the rear of the car and increase the pendulum effect.
Not sure on that one, you'd have to ask someone who has one and races it, I've only got a ZF..... Craig?
One common theme between both styles....
"They're expensive!!!!"
Here's a torsen link
www.quaifeusa.com