the power of the queen compared to other pieces

Interesting question. The actual power of the Queen doesn't change but the player's view of its importance decreases a little as ratings increase.  Larry Kaufman's celebrated study of over 80,000,000 chess positions in the 1990's determined, on average, a Q = 9.75, R = 5, B = N = 3.25, P = 1.

Lower rated players tend to be much less likely than higher rated players to trade a Queen for two Rooks or a Queen for Rook, Knight, and two Pawns, even though it's usually to their advantage to do so.

Well I just started playing this January and there is no way I could win a game if I lost my queen even if my opponent lost his too. I would be totally lost without the queen. Of course my rating is only around 800 though.

I think it depends on where and what the piece is doing. Position has to do with the value of the piece. I think the better you get the more you realize this.