My OCD and other delightful obsession based issues have made me spend far too much on strings over the years but I think I've found a string that I like on all my basses - the Dunlop Stainless Flatwounds.
They are currently installed on all my basses except my Sandberg. That has EB Group 4 flats which I like very much so they are almost there as a control while I confirm my thoughts.
So I've got the Dunlops on a Fender Precision, Ibby EHB Medium / Short scale, Ibby Mezzo (5 and 4), and a Fender Urge 2.
I'm really liking them. Very smooth under the fingers so no noise from that, bright enough for a bit of slap when needed, lovely and low / full when the tone control is down.
I am really hoping that these are "the ones" so I don't have to obsess about them anymore!
For the first hour after installing they feel a bit crap as they still have some manufacturing residue on them. But an hour playing or getting the fast fret out solves that quickly.