University of Oregon is the big sports school, they get the championships in all kinds of sports, so naturally if you're an Oregonian you have reason to cheer for them. Oregon State is the plucky smaller university with less athletic prestige, so often those people in-state who have no direct emotional connection to either college will often choose the Beavers when the schools go head-to-head. An Oregon State baseball championship will get people more emotionally involved than, say, if the Ducks won the football championship. At least on a personal level.