Lets clarify the benefits of either one...
A steel or iron flywheel isn't going to make you faster, but because it has more rotating mass it will basically keep the engine from losing RPM as fast between shifts. This can help when drag racing, but I'm sure there are slews of aluminum flywheels out there being used because..
An aluminum flywheel has less rotating mass, which means it has less parasitic drag than a steel/iron flywheel. This works the same way as any other rotating piece on a car that is made lighter, such as brake rotors/rims, less rotating weight means the engine doesn't need to try as hard to make it spin, and that energy that would have been spent on turning the flywheel is sent to the back wheels. This also allows the engine to rev higher faster because there is less weight being spun up. There is potential to make more power at the wheels because of this, but the biggest benefit is seen in a faster revving engine, which is typically more useful in road racing.
The biggest area you'll see a difference is in driving on the street, where an aluminum flywheel is much easier to stall, because there is a good amount of resistance in a rotating engine assembly...an engine doesn't want to spin freely (you'll understand this if you ever try to turn one over by hand) and so despite the fact that it will rev much faster, it will also drop RPM equally as fast, meaning you tend to slip the clutch a bit more when taking off. Once you're moving there isn't any difference in how this feels, but that was the most obvious difference I've noticed aside from the faster revs and faster RPM drops.
Of the two, honestly I prefer the aluminum. It's just so badass how fast they rev and the take off is something you can adjust to. I've driven and raced both and I really didn't see the aluminum flywheel as being a problem at the track, there never was a point where we said "hey ya know the car might be faster with a steel/iron flywheel".
That said, I have a stainless flywheel in my car because it was better than the stock iron wheel and cheaper than aluminum and I was on a budget. If I ever change my 14 year old King Cobra clutch (that thing is immortal) I really want an aluminum flywheel.