TL;DR AWD performance advantage is often stated as "Moar Grip!" All else being equal, two cars identical in every way, tires, suspension, etc., have the same amount of available traction/grip. When one end of the car, typically the rear in a stinger, has more power than traction available, the AWD system can send this excess power to the other end, putting more usable power to the ground. LSD is an additional component, not specific to AWD vs RWD. Brake based torque vectoring is the worst from a performance standpoint, mechanical LSD is better, and the best is electronically controlled at each individual corner.
The Stinger AWD, and similar systems are great in limited traction situations. Low speed acceleration, slick, wet, loose surfaces, etc., because in situations when the rears only take 80% or less of the available power to break traction, you can now apply an additional 20% of that power and use it to drive the front, which has available traction. Thus you now have more power to the ground and increased acceleration. However once you reach a point where the rear tires can deliver full power to the road without spinning up (small amounts of spin can actually assist with mid corner rotation), then the AWD is no longer beneficial, between the weight and drive train loss it actively reduces performance.
Cornering is trickier. Ideally, to maintain the fastest possible apex speed, you want to be on the front tires limit of lateral traction, using any the available traction for drive at this point necessarily reduces max cornering speed, or results in unwanted loss of traction at the front (understeer). If you have more than the ideal (small) amount of rear slip, and the front wheels aren't overloaded, turning the driven front wheels into the slip, or to the outside of the turn means you are driving the front end wide, not understeer in the technical sense, but same result. Now you are wide of the ideal line. The caveat is that in low speed corners, as you open the steering you need less lateral traction and can use the front wheels for drive again in situations where you can't apply 100% of the available power to the rear tires, resulting in a faster exit.
As a side note, even in low speed corners you pay the piper for the weight during braking and at the apex, but the lower the corner speed, and the higher the horsepower, the bigger advantage you gain on exit. On tight technical tracks this could put the AWD well in front, think autocross and street courses like Monaco. On a track with long straights and high speed sweepers the RWD is the weapon of choice, think Monza or Spa.
This is all paper racing though. Stingers are big heavy, fun cars, and at a road course track day the driver is going to be the deciding factor. Given equal drivers, I suspect the margin would be small and track specific.
So to summarize, Volfy is correct in that low traction conditions th AWD is better, wet, sandy, low speed. But otherwise RWD, in a performance sense is the better option. This is why in drag races, in equal Stingers, the AWD wins from the dig, and the RWD eventually catches and passes the AWD, because the AWD can use more power sooner.