Even in the studio, you'll risk resonant feedback if you sit in front of your monitor speakers with the fuzz on and the volume up. Turn your amp way down or use headphones when distorting your acoustic. In both active and passive pickup designs, the coil interacts with the first circuit it is connected to. Each different type of circuit can affect a passive pickup's tone in various ways. This makes for consistent performance, regardless of what the guitar is connected to.
Active pickups can also drive longer cable runs without losing tone.
Active pickups require a power source, typically a 9-volt battery installed on the guitar itself. The interaction between coil and input circuit can be tailored to create specific tones. As to sound, that's a matter of personal preference. Lots of classic instruments have been built with passive pickups, and many folks feel that a passive pickup's interaction with their various amps and effects plays an important role in shaping their personal tone. Other players may prefer the consistency of an active system.