Formal:
* Competition: This is the most common synonym.
* Tournament: Used for a series of contests.
* Match: Used for a specific head-to-head competition.
* Trial: Suggests a test of skill or ability.
* Strife: Used for a more intense, aggressive competition.
* Contention: Used for a disagreement or debate.
Informal:
* Challenge: Implies a call to action or a test of strength.
* Battle: Suggests a fierce, intense struggle.
* Clash: Used for a sudden and forceful confrontation.
* Rivalry: Focuses on the ongoing competition between two parties.
* Race: Used for a fast-paced competition, often against time.
* Showdown: Implies a final confrontation, often with high stakes.
More specific:
* Sweepstakes: Used for a competition where winners are chosen randomly.
* Audition: Used for a contest to determine who will get a job or role.
* Election: Used for a contest to choose a representative.
The best word to use will depend on the specific situation and the tone you want to convey.