These words are related, but prevent is a stronger word than hinder. When you prevent something, you stop it; when you hinder something, you slow or delay it. When something is prevented, it is effectively halted and rendered impossible: "Do not prevent us from going." "This treaty is designed to prevent war between our countries." To hinder is to delay progress: "Such interruptions will only hinder our reaching a solution." Related words are obstruct, impede, thwart, obviate, forestall, hamper, retard, block, and balk. Both prevent and hinder are often followed by a gerund: "prevent his going," "hinder his going." In such a construction, a noun or pronoun preceding the gerund is preferably in the possessive case; "prevent (or hinder) him going" is nonstandard, his is standard: "They tried to prevent Jock's leaving (not Jock leaving) the team."
Dictionary of problem words and expressions. Harry Shaw. 1975.