I would have expected #2 to be brighter and more mid scooped as well.
Bass #1 is mostly all mellower sounding tone woods, minus the maple board, which probably adds some definition.
Bass #2 is mostly all bright sounding tone woods, minus the rosewood board.
I would have though the poplar was close to alder which is fairly neutral. The maple top brightens things up, but again, I usually find that fingerboard wood is a big contributor in the wood equation. I usually don't like ash as I find it to be rather mid-scooped in my hands (ymmv), and often is a bit deep in the lows and harsh on top. But not always evidently...
Since in the OP it is said to be "significantly brighter", I wonder two things (which I did not see in scanning other responses) - one, is the tonal difference noticed, and as significant, unplugged? If not, then I think what you have is a difference in pickup windings, or other electronics anomaly, regardless of being the same make/model.
Unplugged you can hear some difference. There could be some difference in the pickups and preamp, but they are the same brand/design. Some variation always exists. I've normalized the pickup height between the two, and also have swapped string sets back and forth.
Is that similar to a spherical toast?
No, closer to Powered Toast Man:
