I dont knwo hwo both work. Just know that Active got battery. How to diffrentiate the soudn adn which is better generally?
Active pickups have an inbuilt preamp which prevents signal loss caused by cables, they usually sound brighter than passive pickups.
Passive pickups are mainly a LONG coil of wire around a magnet structure of some sort. The vibrating string changes the magnetic field, which in turn produces an electrical current the the coil. This signal is amplified, then brought through your speakers. With an active pickup, the general structure is the same, but they use a shorter coil of wire (which makes for a weaker signal), which is then aplified internally. This signal usually has a more unaltered sound.
For the most part Active pickups are louder, more "modern" sounding, they are definately some very loud and modern sounding passive pickups though, that's just generally.
I think you might want to do more searching on this board and check out the newbie links that are stickied to the top of this board. They can offer a lot of info that will take much longer to ask. -Eric. P.S. - Hang out with experienced bass players and soak up whatever knowledge you can possible use.