Yeah, diffs are definately working right other than the missing preload in the clutch pack. I think it's in the tyre physics like Scawen said, that we can use the locked better. You have to set the suspension (springs and anti-rolls) so that the inside driven wheel would lift off the ground while turning (meaning stiffer front suspension on an fwd, and stiffer rear suspension on an rwd than on the other end of the car), and like that you can avoid the crazy understeering effect of the locked-together wheels, so you can turn well enough. I suppose the tires can take on much more weight than they should be able in real life. Let's say the FZR is rear weighted as it is, and with stiffer rear suspension the outside rear tire holds almost the whole rear weight of the car while turing, and with downforce as well that is a lot of kgs, which would cause massive tire overload, and a loss of grip, but not so much in LFS. So yeah, its probably in the tires.
But I think adding preload to cluch pack would make it a hell of a lot better, and as it's alrealy faster (but a lot harder to drive) in some cases it would make the drivers use that already, and a couple of shaping in the tire physics would make everything right: locked diff => off road :P