Play the QUEEN PAWN KILL GAME:
Rules:
White is the pawns, black is the Queen.
White sets all 8 of their pawns up on the second rank, as usual.
Black has the queen on the ordinary square.
White's objective is to get a pawn to the other side.
Black's objective is to kill all of the pawns. If a stalemate occurs, black wins.
Now you can see which is better :)
Depends where the pawns are...
If it were a choice between sides in an eight pawns + King (white) versus Queen + King (black) "endgame" and all the pawns are on the second rank I'll likely take the Queen. On the seventh? I'll definitely take the pawns. Somewhere in between? I'll decide based on the pawn formation (assuming that the position isn't set up for a forced mate for black, of course...).
Have all your pawns or your queen?
Personally I think the pawns are such a huge part of strategy as a whole it would be idiotic not to choose them. But statistically you would rather have your queen.