A very good question. This all started (20+ years ago) with wanting something really compact, and having always wanted a Steinberger. I'd had a Warwick Thumb NT and frankly hated it. I have kept my Hohner B2A for decades because it was cheap and compact, but I don't really like it that much. In some ways the bass I've enjoyed the most was my old Westone (?) Rail.
I'm very much interested in stuff that works and keeps working. Something like a Precision would appeal on the basis that you can keep those things running forever because you can always change the parts, but the Precision doesn't really sound how I like it. The Steinberger appeals because if the neck is straight, the neck should stay straight, and if they're still working since the late 80s, they will probably keep working. The Status appeals because the company is around to help, and is in the UK. The Kubicki gives me the willies slightly because it's weird and might be hard to keep alive for decades. I only really want to do this once. I confess I am seduced by the futuristic looks of Steinberger, Status and Kubicki, and I like headless for that reason.
I do still want it compact, and I really like that sustained sound, which to me seems to come from graphite. However, the Kubicki is the best sounding bass I've heard, at least based on the various youtube things I've found.
So I guess headless comes first, sustainy pianoish tones comes next, and graphite in third place. Compact is a nice to have.
On the Kubicki I read that the thing to look at is whether it's 9V or 18V. There's one available at the moment, pre-fender, but over 2k. I guess if a nice XL2 came along for under 2k, I'd struggle to resist.