The difference is culture, not theology. Evangelical culture is overwhelmingly masculine. Catholic culture is overwhelmingly feminine.
I also once heard Catholicism referred to as "Christianty for Introverts" which might explain why I'm so comfortable with Catholicism. While my parish seems okay on this front, I know many parishes are overly feminine, turning men off. ("Faith sharing" is a phrase that will turn men away. As I once said, "I don't share." "Bible study" is a much better phrase to use if you want men to show up.)
A former pastor once gave this as a reason that Catholics should not ordain women: we're already so feminine in style that women priests could be the tipping point of feminization in the Church that drives many men out. Men need that sense of masculinity and male bonding that male priests provide. It's probably part of the reason why the Knights of Columbus are so successful and popular: It's at least one night a month where you can be around men and be religious at the same time. There's just something very manly about sitting around discussing how to help build and strength and serve the parish with a beer in your hand, like we did the other night.