A limited slip differential makes quite a bit of difference in the way a car handles turns.
A limited slip basically does was its name implies, it limits the slip between the two drive wheels. There are two ways to do this, gears or friction (clutch) packs. With gears, you have the option of using a Torsen type of gear arrangment (ala Quaife) or using a viscous fluid to limit the amount of slip. A clutch pack produces friction when there is slip between the two drive wheels, thus it limits the amount of slip. The tighter the clutch packs, the less slip that is allowed.
Now, with gear type LSDs, the general concensus is that Torsen is the way to go. Viscous LSDs are hardly found in high performance applications. Another benefit to the Torsen style LSD is that it is torque biasing. It will actually transfer MORE torque to the outer wheel when turning, very similar to ATTS, however it's completely passive. The problem with Torsen diffs is that one wheel always has to be loaded. If one wheel lifts off the ground, the LSD effect is lost, and the diff acts like an open diff. A Torsen diff will act during acceleration. A viscous diff usually works during acceleration and deceleration.
A clutch pack LSD literally ties the two drive wheels together with friction plates. The amount of friction determines the amount of lockup. The main benefit to clutch pack LSDs is that they work no matter what the load is on the drive wheels. However, this can be a big problem when the traction differences are quite great on a FWD car, as this causes tremendous torque steer. Another disadvantage is that the clutch packs have to be rebuilt when they wear. A gear type LSD almost NEVER has to be rebuilt.
Another problem with a clutch pack LSD is that it can cause quite a bit of understeer in a FWD car if it is a 2 way LSD; i.e. the LSD action occurs during acceleration and deceleration. The understeer effect is less in a RWD, although it is still there. To combat this problem, a 1 way clutch pack LSD can be used. It only locks up during acceleration, and acts as an open diff during deceration. A 1.5 way LSD is a blend of the two.
In the debate between clutch and Torsen LSDs, you will find lots of opinions. For FWD cars that are used for track racing, the concensus is that a Torsen diff works best (hence the popularity of the Quaife for FWD cars). For rear, it's almost a toss up, but usually racers prefer the Torsen type LSD. For drag racing, most will agree that the clutch pack is best, IF the clutch pack can handle the power.
In terms of adjustability the clutch pack wins hands down, as it can be adjusted with different friction plates, and different amounts of preload. This, however, requires one to rebuild the diff to make any changes.
If you want to know more about ATTS, do a search, I have written a ton of stuff about ATTS, and I even wrote a very technical post describing how ATTS works.
One interesting thing about ATTS (as I understand it) is that the the gear biasing (or difference in gear ratios) is fixed at +/- 15%. I haven't quite figured out what this does to the torque biasing, but it appears that the active torque biasing is not variable like most people think. In light of this fact, I would prefer a Torsen over the ATTS setup any day.