To expand on my previous post:
Modern traction control systems brake only the spinning tire in either of those scenarios. This helps all types of differentials except for the locked locker.
Let’s say the traction control sees a wheel spinning and engages the brake at 100 ft-lbs on that wheel.
The open differential, with its 1:1 bias, now can deliver an extra 100 ft-lbs to the pavement. The same happens with the clutch-driven limited slip, and that extra effect is added to the torque provided by the clutches.
The locker is unaffected, and is actually impaired by the braking. But assuming it is functioning properly in the first place, the traction control cannot sense slippage and thus should not brake a wheel independently.
The gear-driven limited slip multiplies that resistance, and now it can deliver an extra 350 ft-lbs to the wheel on the pavement solely from the action of the brake.
Gear-driven limited slips in combination with modern traction control can do impressive stuff, often almost to the same level as a locker. Even modern cars with open differentials and powerful traction control systems can be rather impressive.
But without the capability to independently brake a wheel, a locker always has the ultimate capability.