She beat all of her competitors to win the grand prize. She beat her opponent in the final to win the grand prize. I would say that an opponent focuses on a one-on-one interaction (at least one at a time), whereas there can be many competitors. During a chess competition with many different rounds, you compete against your competitors throughout the competition, but in each game you have an opponent. Opponent is also bit stronger / more dramatic than competitor.

Competitor means you and the other person want the same thing--like a winning a race. Opponent means the other person is trying to stop you--like a fight.