What is the difference between an Anti-Ship Drone and an Anti-Ship Beam Drone?

Solution 1:

The Anti-Ship Drone is armed with a laser, which does damage to a single room targeted randomly by the drone. It also takes the shields down one level if it hits a shield..

The Anti-Ship Beam Drone is armed with a beam weapon, which does damage to multiple rooms along the path of the beam, but which does not affect shields at all. Instead, shields affect the beam, in that each level of shield reduces the damage of the beam. Since the Anti-Ship Beam Drone only does 1 damage per room, even a single active shield can render the Anti-Ship Beam Drone completely useless.