Yes, the left mobilise more. I think that's because protest is more one of their tools. And I think people more to the right view protest in a derogatory way.
Violent protest is more the fringes of either side. I regard them nutters on both sides. And I view them equally as cowardly bully types because they will target the least likely to harm them.
More widespread violence takes a lot to start it. The miners strikes and poll riots spring to mind.