I guess it's okay to clutter up this thread at this point... for the purpose of this discussion, I'll confine it just to my Alembics, or Alembics I've had...
They are are all unique, but with some defining characteristics.
My Persuader 5-string and Custom 5-string are structurally very similar; mahogany core, maple tops, maple necks with 3 purpleheart laminates. Both are medium-scale. Similar electronics. Obviously those two are going to respond a little bit differently under the left hand due to the lack of frets. But the attack and zing of the notes as played, with same-same strings... it's remarkable. Now, the question is, how much of that is me, trying to express myself the way my brain thinks this passage or that should sound?
I had two Distillates. An early fretted one with mahogany body core and walnut top, and an '85 fretless that had a custom Point body and Bubinga top and back. The pickups were located a little bit different too. Those two basses were day and night different to me. I sold them both, but not because of the sound... the older of the two was incredibly responsive. The fretless just couldn't do anything my Custom 5-string couldn't already do at the end of the day.
My two Series basses are also very similar in construction... mahogany body core, walnut top and back, maple and purpleheart necks. The older one of them has a beech center laminate in its neck beam. My recollection of the newer one is that it's much more clear, bright-sounding. My older one is Woody, and warmer. Also considerably lighter. I'm anxious to A/B them again someday.
I think it doesn't matter much which bass I'm playing. I always try to fit into this sonic space that exists in my mind's ears, that just sounds and feels 'right'. Some basses are just easier to get there with.