I believe that once the stern armor is destroyed, Long Cannons would actually be more effective at inflicting damage to cannons and wounds/ kills to crew.
Sure, a Carronade has a large projectile, but it's also rather slow in comparison to Long Guns.
Long Guns mean a smaller projectile, with a higher muzzle velocity, translating in an amount of kinetic energy that is higher, and will be retained longer.
This in turn means (theoretically) higher penetration, and a higher chance the cannonball will travel more distance internally along the length axis of the ship.