Both are large advantages for black as you say. The "old me" would have loved endgames and tried to go out of my way to exchange into winning endgames, so ...Qh5 would have been appealing when I was like 1800.
However, the "current me" barely even looks at the retreating ...Qh5 and sees much more appeal with ...Qd3. The idea of ...Qd3 is still on the d2 pawn to hinder white from developing their queenside pieces. I actually made a video on the "Night Attack" and it uses this same motif in a similar situation:
Would you trade queens here or keep the pressure? Stockfish shows 6 point advantage for black keeping queens on the board. If traded, black is still 4 points up and to me it looks like a clearer game. What would you have done here? Black to move.