CraigC,
My $. 02 It depends! If one wheel has no traction (up on a jack, etc. ) then that is the one wheel which will have drive and will turn, the other will not turn. If however, you are on equal traction terrain, then both wheels will have drive. If you are blasting/bashing along in mud, then you get one side, then the other, then both, on and on and on. Sometimes you can hit the brakes intermitently and it will make the differential try to drive both wheels.
I'm really disappointed to hear of problems w/ the LSD, mine has been great so far. Hope these problems are in the minority. When I first got the truck, I stopped w/ one side off the pavement on gravel and stomped it. It laid rubber on the pavement. I thought that was pretty good performance. Haven't tested it recently, but will now.
RandyN