For rapid fire a heavy should be able to go further before accuracy suffers, though the shorter the barrel, the less this matters. Heavy is also noticably so in terms of handling but fluting handles a fair amount of the weight issue.
Light is light weight, accurate etc, but heavy fire can supposedly degrade accuracy on longer thin barrels. Also excessive heat can increase barrel wear so a heavy barrel 'may' last a little longer under extreme use.
My personal preference in barrels is heavy fluted.