>>535057876
Cannon ships naturally have more shield power than energy, because you need less power reactors for more shield power than energy weapons. Cannons also do more damage against shields than energy weapons outside of the Disruptor.
Missile defeats Gun because they outrange it and can focus critical components. They can also be anti shield EMP or nuke assassins against a dazzled target. Gun also do less destructive damage against unshielded ship armor do to armor penetration and rate of fire. Some ships have anti missile defense but a barrage of HE missiles will always get though.
Railgun beats Missile because it's harder to place shields for effective missile ships and they can't handle damage due to more ammunition space for launchers that consume more missile ammo per shot. Storage rooms are large targets for the Railgun's lack of component targeting accuracy but high penetration will cripple ship internal logistics and crew hallway paths that make up the majority of the missile ship firepower. Crew is needed to reload missile launchers, and dividing the crew to fuel additional shields will lower ship's offensive output.
Energy ships have peak DPS against unshielded flanks and don't have to be large for cannon amount and ammunition storage to be effective, making them smaller targets and easy to pack and outmaneuver against slower and venerable ships. Energy weapons are more precise against components like engines and cockpits.
Railgun ships are highly complex, expensive and crew complement dependent, that can be overrun by multiple smaller and cheaper ships. The crew has to walk around the whole railgun, or even though the railgun loader room to reach the other side of the ship. That include refueling the many engine rooms to maneuver the railgun against its target and the whole length of the railgun itself. Do to that it's highly crew uneconomical to add additional weapons or shields for protection.