I have the anti-spin rear diff in my 2 wheel drive and I was wondering the same thing. Like what is the different between the anti-spin and the same truck, but without that option selected?
2wd wtih no limited slip (open diff) = 1 rear wheel gets power. On flat pavement, you will always have good traction. However, when you get in a situation where one wheel starts to lose traction, all power gets transferred to that one wheel. Before traction control, brake lock differentials, etc., there was an old trick. If you ever got yourself in a situation where one wheel was spinning, you could lightly apply your brakes or emergency brake. This would slow down the free spinning wheel, and allow the other wheel to get traction.
With today's brake lock differential technology, a truck with an open diff acts the same as a truck with a limited slip. Just not as fast. On a 2wd truck with no limited slip, if one wheel starts spinning, the computer senses this, and will apply the brakes to that one wheel. The computer is fast, and can do it quite efficiently. If your truck has a limited slip in the axle, the limited slip does the same thing, before the computer ever has to get involved.
Modern vehicles are light years ahead of 4x4s from the past. As stated previously in this thread, my wife's WK2 Jeep Grand, is a full time 4x4 (essentially AWD), and has open diffs front and back. I've had it on trails that are steep with loose rock/gravel. Basically, I just keep the throttle constant, and the computer does the rest. Every time a tire starts to lose traction, you'll hear it start slipping and throwing gravel, within less that a second, the computer will slow that tire, and traction will be regained. The Jeep might lose momentum for a split second, but then it just picks up where it left off, and continues climbing. It really doesn't take much skill from the driver. Just point it up the hill, and give it some gas. The computer does the rest.