Defense 1 drones shoot down incoming missiles (and boarding drones) and have a moderate cooldown on their shot. If I have two Defense 1 drones active at the same time and a missile is fired at my ship, will both Defense drones shoot at it (consequently rendering having both active at the same time pointless), or will only one of them shoot at it, allowing the other to keep its weapon fully charged?
In my experience, drones will shoot at the first missile they see provided they are off cooldown and are capable to fire. This can be the same missile but doesn't need to be. If you launch both drones at the same time, they will almost become synchronized with each other. If both are off cool-down they will fire at the first missile they see, go on cooldown at the same time, then come off cool-down at the same time, ready to both fire at the next missile.
This makes the use of two defence drones fairly pointless even at the final boss fight. In the case that the second drone is launched just as the first has fired, the time taken between rocket attacks will make sure that both drones' cooldown will become synchronized and they will both attempt to fire at the first missile during the next volley.
Defense drones can miss if they're on the wrong side of the ship at the time. Running two at opposite sides makes that less likely. Keeping them on opposite sides also increases the chance of actually firing at different targets if you're attacked by two missiles at once (Rock ships have an annoying tendency to do this).
These benefits are rarely relevant and are unreliable at best even when they are. You're better off using the second slot for an anti-ship drone or saving the power and the parts for something more useful.
Against the final boss's triple missile launcher, which you mentioned, they tend to sync up and both hit the first and third missiles- same as a single defense I drone. The best defense against the missile launcher is a good offense- take it and the crewmember in it out with boarders and they can't repair it.
Defense drones can miss their target. So yes there is a benefit to deploying two drones at the same time, it reduces the chance of missiles getting trough due to misses by a drone.
Someone mentioned that defense drones can miss, which is true. Defense drones orbit around your ship, and occasionally they will fire a laser at a missile which is approaching the ship from the opposite side. In this case, the missile 'beats' the laser beam and your ship is struck.
All this to say, two defense drones could be useful if they were deployed so that each was orbiting opposite sides of the ship. That way the chance of a missile managing to hit your ship would be very small.