Beaver Creek has the town of Avon, which while maybe not very big, is a "normal" little resort town with a Kroger grocery store, Beaver Liquours, and a decent number of restaurants and hotels - Vail has a more all-inclusive feel with everything jammed up all around the base areas. Breck seems like a larger town when you drive down Main Street, but Avon has a larger population (Avon, Breck and Vail all have populations that only range from 5-7k people, Avon the largest).
You're basically splitting hairs, each spot has a different feel. Summit County vs Eagle, village/chalet vs town. The Beave is notoriously the best mountain in northern CO, Vail the biggest destination, but the Angrysnowboarder will be at Breck spraying your wife and kids in the park...decisions...
Support Local Business
"Shop Smart. Shop S-Mart!" - Ash