Usually the rear end additive is a friction modifier that controls the stick-slip characteristics of the clutch plates or cones in the limited slip unit. If there is no friction modifier, the plates stick until the wheels are traveling at a different enough speed (i.e. turns) until they break loose - you get noise, clunking of u-joints, and probably a "hopping" feel. If you ever put an off-road four-wheel drive in 4WD and tried to turn into a parking spot, you know the "hop." Add the friction modifier and the plates slide smoothly, yet the pressure on the plates keeps both wheels pushing the car forward.
*In many cases* a replacement gear oil may not have any friction modifier and performance depends on whatever friction modifier was in the rear end before - this kind of additive "sticks" to metals and isn't flushed out when you drain the oil. You'll perhaps see warnings that the oil is suitable for top-up, but not replacement.
And, of course, since we've seen how an additive makes a difference in a rear end, I have to add that synthetic oils are not automatically the king of performance; the additive package matters (to coin a phrase).
