Ok, it's time for Jim's "not so popular" opinion: When I began 4 wheeling in 1970 rock crawling was not a fad yet, in fact when wheeling we avoided large rocks like the plague. Eventually rock crawling became the thing, in fact normal trail wheeling no longer gets any press. Rock crawling now means one tire can be in the air most the time, and that's what has made Limited Slip Differentials very unpopular.
(1) An open diff. (no posi) is very lazy, it spins one tire only, the one that will spin the easiest, and never the other. This will not work when one tire is in the air.
(2) An Auburn Gear LSD sends 100% locking pressure to one tire (the one that has the most traction), and 80% locking pressure to the other side (when both tires are on the ground and have some degree of traction on both sides). This happens in 2WD on the highway and 4WD off road. Once one tire is in the air, it becomes the tire that will spin the easiest, so an Auburn LSD sends 100% locking pressure to the one that has the most traction, the tire on the ground.
(3) Full lockers (fully gear driven lockers) are not what we call "highway manageable" (unless they can be unlocked on the highway, ala air lockers). Everyone knows these lockers work well in off road terrain, but their problem is they are problematic on the highway. For this reason many choose the air lockers. Problem with air lockers is they provide zero highway advantage when unlocked.
For the guy who is into normal trail riding (dirt/sand/mud/snow with both tires mostly on the ground) the Auburn LSD would be my pick because:
(1) they are completely highway manageable, they unlock during highway cornering without the clunk/ratcheting/wheel hop.
(2) they work all the time, on or off road, so they have highway posi advantage as well as off road posi advantage.
(3) they provide 100% locking pressure to tire with most traction, and 80% to other side when both tires on the ground.