What Will said, a case by case issue.
A super light flywheel lets the engine rev up much quicker. Great in a light road race car. For driving around town, a heavy flywheel is sooooo much easier to drive. No bog, no stall.
A great big, super heavy flywheel stores -massive- amounts of inertia. This will get you right off the line.
There were two Corvair drag race guys back mid 70's that fabricated a custom flywheel that weighed, so the story goes, 150+lbs. The plan was that the guy driving would rev the car to redline (a five second chore) while rolling up to stage and just slip the clutch all the way down the track. During test runs with various alcohol soaked clutch disks, they learned that, in addition to launching the car like a rocket, the huge flywheel acted like a gyroscope and helped keep the car pointed straight.
The car made one appearance at an AHRA event, running in VS/O F-2 class. The class index record was 17 seconds (the Corvair was a "compact", remember).
The old AHRA had over 400 classes then and if you could get your car to a race, they would either find the right class, or make one up for you. Almost everyone got a trophy...
The car made two runs, both at 12.2 @110mph, and was then yanked for further inspection. Despite being within the class rules the car was disqualified, and never raced again.
Rick