Defining and ranking rivalries is tough and sometimes pointless. Cleveland Browns fans hate the Baltimore Ravens and get annoyed by the Cincinnati Bengals but their feelings toward the Pittsburgh Steelers are different than the other two.
The Steelers are the Browns longest rivals, dating back to pre-merger with the AFL. The two helped form the AFC Central and then the AFC North together but, at least for most people reading this lifetimes, Pittsburgh has long controlled the matchup.
Historically, the Steelers are 81-63-1 against the Browns. Recently, there have been long stretches where Cleveland was lucky to win a game.