The differential gears serve to multiply the torque of the engine at the rear wheels, meaning that,
with traction, you get out of the hole and accelerate faster, usually about a half-second faster after a switch from, say, 3.27 gears (stock) to 4.10's. That means that if your AOD Mustang runs a 15.0 quarter mile, with traction, you could see a 14.5 or close to it. A noticable improvement that you'll be able to feel in the 'seat-of-the-pants dyno'.
Of course, if you
don't get traction it's a lot easier to do burnouts (and fry your AOD).