Quicker revs because of less rotational mass.  Very slight increase in hp due to taking less energy to get the flywheel rotating. 

Decrease in inertia. 

The downside is less flywheel!!!

More stalling at low speeds, less tractor like chugging. I have a YFZ450 that could use more flywheel when the trail gets technical.

leave the flywheel stock and have the crank lightened instead.

A lightened flywheel can make a noticeable improvement in acceleration in 1st gear with its effect diminishing as you shift to the higher gears.

A lightened flywheel does not increase the brake horsepower the engine produces.  It only decreases the energy stored in the rotating components of the engine and will make a little more power available to the rear wheels WHEN the engine is accelerating very rapidly.  When dyno testing, a lightened flywheel will sometimes show a very slight improvement in power before the power peak if the dyno runs are under 2 seconds in length.  The dyno will not usually show any power gain by the time the runs are 4 to 6 seconds in length. 


If you are racing on pavement or where you can get real good traction and your swing arm is long enough to keep the front end down, it could improve your acceleration in the lower gears. The overall acceleration and lap times of 250cc or larger dirt bikes and quads usually suffers when the crank or flywheel is lightened.

Lightened cranks and flywheels always shorten the life of the clutch basket, clutch hub and transmission gears.

leave the flywheel stock and have the crank lightened instead.

Rotational mass is rotational mass, wherever it is located in the system.
Still have the same drawbacks as a lightened flywheel, still have the same benefits.
Although, I'm not familiar with the durability aspect of it...perhaps a lightened crank loses no effective strength whereas the flywheel does?

With respect to kinetic energy, you can get the same rotational inertia with less overall weight by having the flywheel larger in diameter.
A small diameter flywheel has to be heavier to maintain the same rotational inertia.
So, you could effectively cut the weight of the flywheel in half if you enlarged the diameter while maintaining the same inertia.
Sucks that this aspect isn't practical on our quads, because you could use the newer style stators in 4 strokes to get more watts and less total weight.


Personally, I'd like to see how a heavier flywheel would work.
Easier starting, smoother running, easier to lug around trails, maintains RPM better over choppy surfaces, more inertia going to the tires when you rev up the engine and dump the clutch...there could actually be a lot of benefits.
A heavy flywheel spun up to RPM is like storing extra HP for a short burst, so instead of being able to launch with 90HP you might launch with 95HP, then settle back down to 90HP as soon as the flywheel matches the tires in speed.
Remember those push car toys that had a flywheel inside them?
You could rev the **** out of them (protip: use a grinding wheel to spin the tires up LOL), drop them on the floor, and watch them do wheelies, bounce all over the place, knock down cats, and climb up walls with nothing more than stored flywheel energy.
Now, take that concept, apply it to a race quad with a heavier flywheel, and you'll see where I'm going with it.
At the very least, it would be a shoe-in for getting the holeshot!

A lightened flywheel is only practically beneficial when you don't have a load on the engine...it takes less time to spool up to RPM before you dump the clutch.
I don't know what the figures would be on actual acceleration under load, they would be measurable of course, but I would imagine the gains are hardly noteworthy and probably not worth the drawbacks associated with them for anyone excluding maybe high-strung drag racers.
That's my opinion/theory on the matter...with no empirical data to back it up, it could very well be a "good in theory, bad in practice" pipe dream.