Aluminum will reduce the rotating mass of the assembly therby allowing the engine to rev quicker. It doesn't store as much kinetic energy for accelerating the vehicle from a stop, so you have to raise the rpm and/or slip the clutch a bit more to get moving. If you have a real torquey engine, it can be tolerated on the street easier than a less torquey engine. The torque makes up for the reduction in stored energy in the flywheel.
I am not sure of the physics to back up that statement.
In an automatic car a smaller torque convert (actual dimensions) is used in racing events where you want acceleration off of the corners because there is less weight/mass for the engine to have to accelerate. This enable the engine to rev faster because it does not have to swing a big heavy torque converter. The physics would be the same with a flywheel. An luminum one being lighter would let the engine rev faster, its less weight for the engine to have to turn.
"Stored energy" would be in keeping the engine spinning with momentum of a heavier flywheel. With a heavier one the engine would not slow down as quickly when you let off the gas as the greater mass would have more momentum.
Steve