Imo, each weapon type is well designed and balanced in STO.
Beams vs dc/dhc: less dps but miss less and have a wider firing arc. They can deliver massive dmg with BO. FAW provides higher dps, but the dmg is diluted when there are too many targets.
Cannons vs dc/dhc: less dps but higher firing rate/arc. Higher firing rate means more bolts hit the target, resulting to have more chance to hit when the shield is down. Hence, in some case more dmg than dc/dhc. It all depends on the targets.
Dc vs DHc: about same dps/firing arc. Dc has higher firing rate but less dmg/bolt than dhc,
Turrets provide a constant extra dps. (more useful with cannons setup due to the boff skills.)
Torpedos: low dps but deliver massive dmg.
Each type of weapon has pros/cons, but most of the pugs have stationary or slow moving target. Hence, dc/dhc are more useful than others. In pvp, it may not be so since pvp is all about player skills. If you got wacked in pvp, it just means you don't have enough skills or wrong/bad equipment.
i did some testing.. on the same ship.. doing the same missions. with little to no boff powers. 125 weapon power.
DHC/turrets are top. like 4000 dps
DBB/turrets are just under it. around 3800 dpp
and straight beams are way down.. like 1400 dps this was trying to broadside as much as i can.
you can bring the dps tho back up, to around 3500 dps with aux2bat, eptw and bfaw, but i didnt use those skills with he cannons
[12:35] Vessel Two of Two Unimatrix 01 deals 225232 (271723) Plasma Damage to you with Plasma Lance.
[12:44] Vessel One of Two Unimatrix 01 deals 1019527 (1157678) Kinetic Damage to you with Plasma Energy Bolt Explosion.
They're not horribly imbalanced. I've killed every type of ship with my Galaxy-X (Considered to be one of the worst ships in the game) and that includes the Bugship (The best). I really do wish that beam weapons were more powerful, but at least they're not as maligned as ground weapons are.