The Pass is warmer in the midbass and midrange and slightly smoother in the top end. It's a beautiful amp in almost every way, the only issue I had is it didn't have a firm grip on the woofers of the Sophia 2.
With the Bat, the bass is tighter and not as bloomy (or muddy), so the end result (at least in my room) is that the soundstage is more open, I hear more air, etc.