Not that I have any experience on the matter, but my logic would tell me that I would use a heavy flywheel with slicks and a light flywheel with street tires. The heavy flywheel could be used to store energy before the launch, but you would need slicks to put all of that energyto the ground because it will dissipate quickly. It will also make you less likely to stall the car at the line and may also help with consistency for bracket racing. A car with a heavy flywheel isn't going to peg the rev limiter as quickly if you lose traction, giving you a little more time to react with the throttle. The heavy flywheel helps tame peaks in your powerband which might otherwise cause you to spin the tires.
As for light flywheels, they give you better throttle response. If you do lose traction, you can stop the tires spinning more quickly with a light flywheel because it has less inertia. A light flywheel makes shifts faster because it takes less time for the engine to slow to the rpm of the next gear.