I think part of the difference here too is the size difference and how centralized the Vatican is. Sexual assault, and subsequent covering up, is definitely happening in schools (public, private, etc) at a rate that's not unlike the catholic church. And yes everyone involved in such cover ups should be fired and sued.
I agree but I will add the money element to it. The Vatican/Catholic Church is one of the wealthiest institutions in the world, they go to great lengths to protect their money and influence.