This is a difficult question to answer, which is why all this stuff comes up so much (e.g., does 'wood' matter, 'what's the difference between maple and RW boards', is 35" scale better for B string, etc.).
The simplest way to think about this is that a bass is a complex machine, and the tone, playability, etc. is a result of the interaction of many things... the wood type, the resonance of a particular piece of wood, the construction method, the density of the body, the mass of the headstock, the pickups, the impedance of the output of the instrument, the scale length, the fret material, the finish, etc., etc.
No one thing really seems to drive the way different basses sound, or the way a B string feels... it's the combination of all the above.
I've played ash/maple active basses that were muddy and dark, and alder/RW passive basses that sizzled and growled. I've played bolt-on basses that sustained forever, and neck throughs that have had the quickest, punchiest attack ever. I've played a 36" inch scale bass that had a lame sounding B string, and many 34" inch scale basses where the B string was huge, taught, and articulate.
The 'brand' thing is more a reflection of consistent, high quality construction versus not. So, in general, the Fodera brand of basses will have 'better' B strings than off the shelf Mexican Fender 5's, (as an example). However, I've played Fender 5's that were magnificent, and I've played a Fodera or two that had problems.
It's also why two basses that seem identical (same preamps, strings, pickups, body woods, etc., etc.) can have VERY different B string tones and feels.
How's that for a long response that doesn't really answer the question
