The different thickness of oils that can be put in the diffs make a difference in how they disperse the power, thin oil will let the wheel with less grip or resistance get all the power, while thicker oil will make power go to both wheels, the thicker the oil the more evenly the power is distributed, making them like a limited slip diff in a 1:1 carb, better for traction.
How thick or thin your diff oil is will depend on the type of surface you drive on but the different thicknesses can also effect the way your car handles & corners to.