While there is no mechanical influence on the game (a three-star monster is not 'stronger' than a one-star monster or anything), it may influence your decision in what star rank card you want to pull next. For example, if you see that 3 three-star monsters are out (as all the monsters are revealed face-up on the play table), then there is only 1 three-star monster remaining in the dungeons, so the blue three-star cards are relatively 'safe' to pull from the dungeon.