In a caber toss between Saruman and Treebeard: Treebeard wins by successfully tossing not only the caber, but the entire Tower of Orthanc as well.
In a fishing competition between Sméagol and Déagol: Déagol takes an early lead by actually catching a fish while Sméagol sits on shore, but is murdered by Sméagol and thus disqualified.
And
in an arrow-catching competition between Boromir and Faramir: well, that's just harsh, isn't it?