Additional info here (and cast your vote).
This is a tough one for me. It's hard not to vote for one of the three "grand slam" winners (see yesterday's comments), so I'm going with the film on the left. But I won't be surprised if David Lean's epic masterpiece wins this match, especially given the year in which each film was released (1934 v. 1962).
Most lawyers have a great affection for To Kill a Mockingbird, and rightly so. But few remember that it was Lawrence of Arabia that took home the prize for Best Picture that year, beating not only TKAM, but also The Longest Day, The Music Man, and Mutiny on the Bounty. In the Best Actor category, Gregory Peck won the Oscar over four other nominees, including Peter O'Toole. It was the last of Peck's five nominations (and his only win). It was the first of eight nominations for O'Toole, who has yet to claim the prize.
Yesterday's result? On the Waterfront (59.8%) defeats Titanic (40.2%). Next up for On the Waterfront? The Godfather (or Brando v. Brando, if you wish). I see The Godfather running the table on its side of the bracket and advancing to the final faceoff.