IMO, a conventional limited slip has an advantage over a single drive wheel when the limited slip is seeing the same, or close to the same taction to both wheels.
This is because a conventional limited slip transfers most torque to the wheel with the least traction.
A torque sensing limited slip differential does the opposite (more below).
So ..... if using a conventional limited slip differential in a situation where the right wheel is in mud and the left is on pavement, the traction is not going to be as good (in this same scenario) as a single driven wheel system that has it's drive wheel on the left, and vice versa for an opposite scenario.
But also because you still get 'some' torque to the wheel that has the most traction with a conventional limited slip diff, it (in practical use) has an advantage over a single drive wheel because in most situations it will provide some traction to the wheel with the most traction where a single wheel will leave you pushing if the drive wheel is in the muck.
As indicated ....... the best limited slip drive system is a torque sensing system because it is constantly applying the most torque to the wheel with the most traction, in a way that proportionaly matches that traction at any time.
Biu I don't know of any trike kit using a torque sensing diff.
They are heavier, more complicated and more expensive than a conventional diff, and really not needed on a trike.