There are three types of limited slip differentials. One design uses cone clutches, another has multi-disc clutch plates like an automatic transmission clutch pack, and the Detroit Locker differential has metal teeth that positively lock when power is applied in a turn and one wheel tries to spin. The Detroit Locker is EXTREMELY noisy. Cone clutch differentials pop and shudder a lot unless exactly the right amount of lube additive is used. Disc clutches don't usually give any problems, but they're probably the least effective of the designs at actually equalizing torque in a wheelspin situation. Chances are you've got cone clutches, and you need to add a bit more Moose Juice!
Jerry