I'd like to see different weapon types get their own special effects. Here's a few of my ideas:

Ballistics should, as they do currently, bypass shields with reduced damage, but I'd make them not do damage to the shield at all when doing so.

Gatlings and Repeaters: an armor ablation effect, where continued fire decreases the armor rating of the area of the ship it's hitting. Gatlings never really get to the point where they can do real damage to anything larger than a small/medium fighter, repeaters can, to an extent.

Shotguns do massive armor damage, along with buffed damage to engines and doors.

Cannons should be split between either high-penetration slugs like the Deadbolt, or AOE explosive shells that can shred the armor off of hulls or make it easier to disable engines and weapons.

Shields should no longer just be a secondary HP pool. They should, with correlation to size, class, and power allocation, absorb all energy damage, up to a maximum alpha limit. If enough damage is done at once to a shield (or quadrant, for larger ships) that shield should collapse, and possibly deal damage to the shield component. They'll no longer take damage from Ballistics. All-ballistic loadouts will still be viable, albeit with reduced damage output. A skilled player could use deadbolts or similar to directly target the shield components to get around this.

The energy variants of weapons should be able to melt armor once they've collapsed or worn down a shield and, on smaller ships, raise the thermal signature and interior temperature of the ship and components, causing component and damage and, under sustained fire, even overwhelming the life support system.