"Active" means it has lower output impedance, the pickups are electronically isolated from other devices (meaning they won't affect each other's behavior) and sometimes means it has higher output. The impedance is not usually a factor WRT effects, but it's huge when dealing with most vintage-style fuzzes, because it's in the nature of those fuzzes to sound best when they are interacting directly with passive pickups that have "high" output impedance. Isolation is part of that picture too, with vintage-style fuzzes, but not a factor with any other effects. Lastly, there's the output level. Again, not all active basses are "louder" than all passive basses--but it's common enough to mention--and the volume (amplitude) of your signal can definitely change the behavior/tone of your effects. Dirt effects will be driven harder, envelope effects will trigger sooner (and stay triggered longer), and various other effects can just sound better or worse in some general way.
That's about it!
