In a riddle contest between Bilbo and Gollum: Gollum would win, because, well, for being a tormented and wicked creature with an abnormally long life corrupted by the Ring... he at least played by the rules and asked riddles and not questions. Geeze, Bilbo. Gawd.
In a figure skating competition between Boromir and Gothmog: (Though an interesting crosssection) Gothmog would win, considering Boromir OBVIOUSLY tripped over nothing (as far as the judges could see) and was generally sloppy. Gothmog, however, even though he melted the ice through and found himself splashing in the suddenly boiling water (which led him to nearly incinerate the judges) rack up enough pity votes to win Miss Rohan were it his goal and, therefore, won.
In a rock climbing contest between Aragorn and a Moria Orc Aragorn, who'd barely leave the ground by the time the orc was 15 feet over head, would win because of the misfortunate destruction of said orc's life due to the interferance of that bow-twanging git, Legolas.
In the "Scariest being in Middle-Earth" with Sauron going eye-to-head with Bilbo Baggins: Sauron would suffer a crushing defeat by the ancient hobbit. Sauron is expected to be frightening... Bilbo just keeps becoming more and more like a one halfling horrorshow. (Scared me'h so bad...)
In a head banging competition pitting Pippin against Haldir: Haldir would win expecially if Gandalf were one of the judges... who'd say that Mister Took needs far more practice against the Walls of Moria.