Quaife, Wavetrac, Torsen, Dinan (basically Torsen) are all gear type LSDs, while OS Giken and Drexler are clutch type.
The clutch types offer performance advantages on a track, but aren't as nice for day to day driving. They're still fine for the street, but it's up to you if they are not quiet or smooth enough if you're daily driving your car. The quaife and wavetrac are both great for street driving and track days.
Basically, for the street a gear type will cost less money, be less work for you to maintain, be smoother, and overall nicer mannered. But a clutch type will hold traction better, will handle high amounts of torque better (no gears to break from too much force), and will overall perform better. Also, IIRC, Drexler (clutch type) manufactures the differentials for AMG cars and for BMW Motorsport's race cars. I don't really know any race cars with gear type LSDs.
I don't have an LSD yet, but I have my eye on the OS giken unit... but it's two grand
I heard it's not terrible at all for daily driving, and has more than double the plates of the Drexler unit so it will last much longer even with hard driving.
I believe the Berk Technology time attack car uses an OS Giken unit. I'm sure someone would be happy to comment on how they like it if you send them a PM.