As far as I'm aware EMG are one of the only active pickups widely used on basses. Think of 'Active' as meaning 'powered'. EMG Pickups actually use power from a battery source to operate. They are very very quiet, and have their own sound.. The advantage of them is how quiet they are, and are favoured by players in high intensity environments where noise can cause a problem.
Lots of the time people call a pickup 'Active' but it's not. It's usually a form of humbucker, which operates like a normal magnetic pickup, but due to the deign and resistance of the magnets, can have a lower output. Used passive they can be too quiet, and don't have that 'Traditional' tone expected from a passive bass. So they are usually married to a Preamp which is 'Active' so it will, A)Increase output and B)Give better tone shaping.
It's about noise rejection, and tone shaping. It's rare to find Active pickups, but especially on bass, they will also have an active preamp, and take their power from that power source. More commonly its 'insert pick up type here' (not active), married to a pre amp onboard. My favourite sound though is always a really good sounding passive bass with a pair of single coils..
Hope that helps (sorry if it's clear as mud!)