Which aspect of literary criticism deals with whether the author's message is significant or worthwhile?

The specific aspect of literary criticism that demonstrates the author's message as significant or worthwhile is the author-based approach. It is also called the Expressive Theory. It depicts that the best interpretation of a text (poem, novel, fictional stories, etc) comes from the author himself. 

The reader-based approach is not entirely reliable because every reader may see a text in a different perspective. There are even cases wherein readers interpret a text in a deep, deep way while the author meant everything in the literal sense. Everything varies from case to case.