100% ^^
How a particular bass sounds in the mix may actually not differ that much but, equally, there's an unmistakable signature sound to some of the greats eg John Entwistle. For me, the quality of the pups and electronics makes the biggest difference here. YMMV!
Playability of basses on the other hand is another thing: weight, balance/neck dive, string spacing, neck thickness, how a bass sits on your frame etc. Can individually, and certainly together, make a real difference to how comfortable and enjoyable a bass is to play.
Would it be fair to say, as a rule of thumb, that the really budget basses don't major on playability? But also that playability won't necessarily improve much beyond midrange bass prices and you then start increasingly paying for branding and/or craftsmanship of boutique basses?