Okay, so active and passive pickups. The question for the ages.
Passive pickups use magnets wrapped in wire to conduct the vibrations of the strings into electrical impulses transmitted to your amplifier. They take on the characteristics of the guitar - the wood (or combination of woods), finish, mass, etc, all affect how the pickups sound. If you take your favorite guitar - let's say my PRS with a mahogany back and maple top (like a Les Paul and a million other amazing sounding guitars) and put those pickups into an Ibanez with a basswood body, it will sound very different. Better or worse is up to the player, leading to millions of "tonewood" arguments in internet forums and after gigs.
Active pickups use something similar but technically much weaker, and have onboard electronics and an external power source (9 volt battery) to boost them. Active pickups ARE their own sound. You can take active pickups out of that PRS and mount them in a lead pipe with strings - literally - and they will sound exactly the same.
If you crave consistency, and want the same "my tone" no matter what guitar you play, actives might be for you. This is why a LOT of metal players love them. Tight, crisp, consistent workhorse pickups that, with their boost, are very high-output, smooth-sounding pickups.
If you like tonal variety from guitar to guitar, and like a little more dynamics in your playing (less compression), and a warmer overall sound, passives are your jam.
I typically do not recommend people have both, and they usually find out why if they try. Active pickups don't "breathe." They have a very tight, consistent tone to them, and you need to add "air" in the form of reverb, especially on clean tones, for them to sound good. Especially if you're used to more classic-sounding passive pickups. It's jarring switching from an active pickup guitar to a passive pickup guitar on the same rig in the same playing session. That's a huge part of why most players use either one or the other - so they don't wind up messing with half their tone every time they switch guitars.
Cut to the modern era. Fishman Fluence. These are a HYBRID. They are very much a big-magnet, wound passive pickup, but they also have the electronics to make them active. You can usually switch between active and passive with a switch or a push-pull volume or tone pot. This is what I have in my Kiesel. They're really quite good, though they do still sound a bit sterile. I find them to be an excellent compromise for the metal player who doesn't really like actives like EMGs. I find that they still play well with my stable of passive-pickup guitars. They still breathe.
Happy to answer more questions.
