They are active yes, but due to their design they sound like passive pickups. All the dynamics are there
It's a completely different design to classic wire-wound pickups. They're great.
You don't have to route a battery cavity, they also sell batteries shaped like spring cavity lid on Strats, so you use it instead of the lid. There's also a smaller battery you can just mount wherever you want, cut out a part of the lid and mount it there. No routing necessary.