Karl, I think we are both explaining the same thing in different ways and I agree, if you give it too much throttle on solid ice, both wheels will spin same as an open diff would. But thats not an inadequacy of the diff.....those beemers would be just as shite without an LSD, its the fact they have way too much power to weight for such circmstances - ditto the T2 has too much torque if you floor it. Slow and easy is the key on icy stuff. Thats why the advice with 4WD is 'engage it but drive as if you had 2WD'.....
But if you are in a situation where, for example, one wheel is in a slimy mud puddle with zero traction, with an LSD you do still get traction on the other wheel, unlike an open diff wich would be losing all its power to the spinning wheel. So in mixed conditions it helps a lot.
Thats also why I think you'll find an LSD in a 4WD is differently geared to a sports cars LSD, the latter doesn't scrabble about on corners etc in the dry like ours does:doh.
But nothing helps on seriously slippery surfaces....thats why I stuck that warning up earlier for peeps new to 4WD....it isn't a 'get out of jail' card!