Heavier flywheels hold more inertia. That inertia helps the car get going from a stop much easier. Since our cars already lack torque, it makes getting the car going from a stop a little more difficult (i.e. you have to slip the clutch more). This does increase clutch wear to some extent. The benefit of lightweight flywheels is that the lighter rotating mass allows the car to rev up a little quicker, however this also means the revs fall quicker as well. Those benefits are idea for putting the car on a road course.

I have a lightweight flywheel, underdrive pulleys, solid motor mounts and a puck clutch. It's one pain in the **** to drive around with on public streets. However, the setup's intent is really for road racing.

 

The flywheel is basically a energy storage device, the heavier the flywheel, the more energy it can store(higher inertia). Which is good for cars that want/need more power to accelerate from a stop, such as drag racing. Lightening it will create less inertia at launch, but you'll accelerate quicker through the gears. So when your at dead stop, the RPM's will drop much quicker, which is what some people don't want to deal with on a daily basis. Also if your drag racing you want some happy medium where you have enough flywheel mass to get you off the line(good launch), but not so much that it hampers acceleration. (search the drag racing section and I'm sure you'll find plenty on info). In road racing your rarely starting from a dead stop, so having the lightest possible flywheel is a good thing. It may chatter at low RPM's, I personally never noticed because my car had clunks/rattles and straight exhaust into a Greddy Ti catback. "Grabbier" would be from a stronger pressure plate(one less friendly to riding the clutch), unless your referring to the RPM's dropping quicker due to the flywheel itself...Hope that helps.

And Mahjik beat me to it..

 

Thanks guys