Synonyms for rival

These verbs mean to seek to equal or surpass another. Rival is the most general: “His ambition led him to rival the career of Edmund Burke” (Henry Adams).
To compete is to contend with another or others to attain a goal, as a victory in a contest: Local hardware stores can't compete with discount outlets.
Vie, often interchangeable with compete, sometimes stresses the challenge implicit in rivalry: The top three students vied for the title of valedictorian.