The main purposes of having an LSD in the rear diff of an AWD system is to aid in handling when applying power when coming out of a turn, to get power to the ground in an efficient manner in slippery conditions and in straight line acceleration with really high power applications. The Stinger has a decent setup. You have the center diff which applies power front and rear as needed. As the rear wheels lose traction, it sends some power to the front wheels. The front and rear diffs are "open" differentials. If one wheel on a particular axle has traction and the other is on a slippery surface, all the power gets sent to the wheel on the slippery surface. So if both front and left rear wheels are on ice and both right wheels have good traction, the wheels on ice spin like crazy and the wheels with traction....do nothing. Enter brake torque vectoring which is what the Stinger has and most affordable awd suv's have. If the wheel on a particular axle starts to spin like crazy, the brake on that spinning wheel is applied to such an extent that the open diff sends power to the wheel with traction. SOME of these systems are ok but they do prematurely wear on the brakes and heat them up. These systems are more reliable and durable as they have less moving parts and are easier on axles and universal joints. They are also cheaper to build. Other systems use limited slip differentials (LSD's). With an LSD, when a wheel starts slipping, the LSD shifts power to the wheel with traction. It doesn't use the brakes to do this, there are clutches and/or other mechanical parts that redistribute the power. With some of the more expensive vehicles, when you go on their websites to build your vehicle, there are options to add an LSD to the rear diff of some of their AWD systems. So not only does the power go from front to rear but ALSO side to side, usually with just the rear end. They could also do it with the front but it adds stress to the axles and universal joints. In some systems, they can apply all power, if necessary, to one rear wheel if that's the wheel with traction. This has obvious benefits in slippery or off road applications but also helps on a track. Especially if it's been raining. Let's say you're accelerating out of a left hand turn on a race track. The weight of the vehicle shifts to the right side of the vehicle. In particular, the right rear. With open front and rear diffs, the left side front and rear wheels may start to spin with the power being applied. The Stinger will apply the brakes on those spinning wheels to try to divert power to the right side of the vehicle to accelerate out of the turn. With an LSD, the brakes aren't applied and it will redistribute the power to the right side wheels where the weight has shifted to. The brakes aren't being applied so the engine isn't fighting the brakes as the brakes are slowing acceleration, the brakes don't wear as quickly AND the brakes will be cooler so they won't fade when you need them to slow before the next turn.
I think I got everything. Someone let me know if I made a mistake but this is my understanding of this. I hope this explains things.