I'm not sure those are actually opposing positions. I believe that a stronger split is how important it is to stop the behavior. Imprisoning somebody will immediately stop their behavior and will provide safety for their victims, but we don't want to use an extreme tool like prison to solve a minor infraction (like, say, shoplifting). It seems to me that the debate is often about what is appropriate, where what you describe as "Approach 1" people prefer to err in too strong a measure that makes sure the behavior is stopped, while others prefer to err on the other side, i.e. is it more important to allow a bully to go to school (or live in freedom within society for larger issues), or is it more important to protect other students from them, and how much bad behavior do we accept, how many chances do they get to alter their behavior etc?