The main difference between a problem$-$based case method and an authority$-$based case method is:

The problem$-$based method focuses on critical thinking, and uses a problem to stimulate reflection on appropriate actions and policies. The authority$-$based method is a study of how decisions are made; it involves attempting to understand a judge's reasoning.

The problem$-$based method is purely legalistic, while the authority$-$based method is primarily business$-$oriented.

Problem$-$based case method is functionally identical to authoritybased case method.

The problem$-$based case method is actually a sub$-$category or type of authority$-$based method that emphasizes critical thinking.