Limited Slip Differentials:

What do limited slip differentials do? Limited slip differentials(LSDs) behave similarly to lockers by tying the two axleshafts together. If one wheel starts spinning, the LSD automatically forces some of the power to go to the opposite side, so that both wheels will try to turn. LSDs replace the differential carriers, and can be as difficult to install as "full" lockers

How are they different than lockers? Since LSDs don't completely "lock" the differentials, only some of the power is shared. This means lockers can be of a lot more help in some situations when you need more power to each wheel. If you have one wheel stuck in something, and one wheel in the air, it's possible that the LSD won't send enough power to the stuck wheel to free it, and you will end up just spinning the wheel in the air. However, LSDs are usually better behaved on road or in the snow than automatic lockers, with less sudden changes and a more gradual transfer of power.

So when would I want an LSD? LSDs can be better than an open diff on the road, so if your Jeep is usually on the road or in the snow/ice, an LSD could be the best choice. They can also be cheaper than lockers.
Many Jeeps also come with LSDs in one or both axles, usually the rear, this combined with a locker up front is popular as the LSD gives you benefits on the road and some assistance off-road, but you still have a full locker up front when you need it.

Anything else? LSDs are less stressful than lockers on weak axles, like the TJ's Dana 35, so LSDs can be a good choice if you don't want to upgrade or change your axles.