Functioning of limited slip vs standard diff in the snow

This may be a little off topic, but

I was driving in the snow today (my '91 bird, not the classic) and going up hill, the tires are slipping (of course). Left, right, left, right, keep it lightly on the gas and find your way up the hill (aka parking ramp of course).

Now, I heard limited slip will send you end over end if you are not careful. However, a standard diff will fish tail all the way on you (like mine does).

If you have a limited slip diff, and you go slow enough, shouldn't it keep you going and from getting stuck without the fish tailing? (ie the reason it is on option on off roading mudd monsters) Ok, maybe a little fish tailing, but not as much?

I guess I don't understand how a limited slip helps in the snow/mudd vs a standard diff.

Is it limited slip keeps you going, but if you lose it, bye bye and a standard diff is more forgiving but more prone to getting stuck?

I kind of got thinking about this from that big limited vs standard diff thread a few months ago, but now that snow hit, I find my self wondering about the other option and if it is better or if the grass is always just greener on the other side of the fence.

P.S. I have never driven a limited slip car. So feel free to school me on the topic. Thanks.

Thanks, these were the answers I was looking for. And the thread you suggested, was the one I talked about in my original post. I read that thread, but it didn't talk about limited vs posi to snow/mudd, but it did include a few stories.