The main characters of each story, Charlie and Hamlet, have death on their minds at the start. Hamlet has lost his father and Charlie's friend has committed suicide.
Insanity is a focal point of both stories. Everyone is concerned that Hamlet is crazy. He is acting very strangely, and the reader at times isn't even sure if Hamlet really is nuts or if he is still pretending to be crazy. His "crazy" is so convincing that his girlfriend is even convinced. Like Hamlet, Charlie has a mental breakdown. The difference though is that there is no doubting Charlie's mental state.
Both Charlie and Hamlet have families that appear to be loving, but there is some gross stuff going on, too. Aunt Helen molested Charlie, and Hamlet's mom was likely having an affair with his uncle. That would explain her quick marriage after her husband's death.
Both stories are about the main characters growing up and taking control of the events around their lives. Sadly, though, Hamlet ends in tragedy and a lot of death. The Perks of Being a Wallflower ends on a much brighter note with Charlie wanting to continue his positive growth.