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A pirate base is larger than a Battle Station.
Unlike Battle Stations, a Pirate Base will not spawn as a result of activity in a sector.
Reports indicate that while a base can be defeated, it cannot be destroyed. 
A pirate base is a large scale (Raid) battle with multiple layers of defenses.
There are certainly missions and scenarios that work for both. The battlestations that we’ve shown so far can be taken out by a wing of pilots, however as you go further into the game, you are absolutely going to want to bring a few more friends along. Also in terms of PVP, we want to plan out some HUGE battles. Those will be perfect scenarios for squads to take on. -- Nicole "Awen" Hamlett