The damage pulse missile was just too slow. In addition, its reload was just too much (3x the amount of the damage beam missile), combined with it doing less damage to shields. When I face ships of this size, I would not expect to require a damage pulse missile to break through the hull and destroy the core, because the damage beam missiles still make decent hole. And they also travel faster, have larger range, do more damage to shields and have a shorter reload time.
