Six-inch versus 5.5-inch secondary guns

Would dropping the secondary battery from 6-inch to 5.5-inch guns be worthwhile against destroyers?

A 5.5-inch shell could do most of the work, but the extra striking power of a 6-inch hit is preferred against destroyers.

The question follows immediately from the need to strengthen anti-destroyer fire after the update. A 5.5-inch shell could perform much of the same work as a 6-inch weapon against small combatants. The larger shell is still preferred because a destroyer struck by it is unlikely to remain effective. The choice is between a weapon that can do the job and a larger shell with greater destructive margin.