A gaming system that provides a player symbol set selection feature including a plurality of simultaneously displayed separate player selectable symbol sets for a play of a game. For the play of the game, enables the player to select one of the displayed symbol sets and after the player selection, the gaming system determines and causes each of the symbol sets (including the player selected symbol set and the other non-player selected symbol sets) to display a separate randomly determined outcome for that symbol set for that play of the game. The gaming system provides the player any determined awards for the player selected symbol set and additionally compares any determined awards for the player selected symbol set and any determined awards for the other (non-player selected) symbol sets for that play of the game. Based on that comparison, the gaming system can provide the player one or more comparison awards.