Hehe, I must admit this hypothetical situation is starting to sound rather silly, like one of those geek conversations about pitting two unrelated superheroes or supervillains together to see who'd win in a fight.
But to get it a bit more serious, how about the Civil Rights movement? Sure, there was a lot of violence involved on both sides, but some of the most famous examples and imagery in the movement were peaceful protests and marches led by people like Martin Luther King against violent police forces, yet the Civil Rights Movement was regarded as successfuly eventually. Their peaceful methods overcame the violence of their opposition.