About 73 million people visit YouTube every month, according to the traffic-monitoring firm Compete. Vimeo gets just a tiny fraction of that horde, fewer than 3 million. But the content looks like it comes from the Web’s most talented lot. Vimeo attracts a high-art, film-buff set—the kind of people who, when making movies for the Web, pause to consider such virtues as cinematography, framing, music, and composition.