Part of it is the old HAZ Lab preamp. Part of it is that they're just great basses. Made in USA, neck through, nice woods, a very interesting and ergonomic carved/curved body, fancy inlays, nice hardware, rarity, etc.
I've got an 80s NS-2A (made in Korea). It's a fine bass. Light weight and balanced. These ones used "plain" maple, rosewood fingerboards (not pau ferro), black hardware (not gold), and instead of EMGs, some kind of passive Spector branded pups and a Korean HAZ knockoff. I picked it up at a pawn shop about 8 years ago for $200 with a Peavey T40 case (Anyone need a T40 case?). I replaced the electronics with EMG pups and pre. I pretty much only use it for cover band stuff, but again, it's a fine instrument.
I always get a chuckle about the Sting connection. He used his for literally one tour (Syncronicity). Not sure if he recorded anything with it.