Short version: The in-game DPS figures don't take into account how the energy drain system works in practice (and I'm not entirely sure that even the Cryptic devs understand this). The DHCs are much more energy efficient because they spend a larger percentage of time in cool down where they aren't draining power. Weapon power also doesn't seem to drain instantaneously, and DHCs have more of their damage front loaded which means they inflict closer to full damage (energy hasn't had time to drain out yet).
For more detailed information see my guide linked below. If you want to see how different weapons perform together, it's easier just to use my Starship Weapons Calculator, which is fairly accurate based on the tests I ran to verify its results.