How does Hamlet's conclusion on the question of "To be or not to be" develop the reader's understanding of his character

In Hamlet's soliloquy he discusses death, it's pros and cons, and consequences in depth. His conclusion, that the dreams death may bring are too frightening to face, characterizes him as a coward as well as an intellectual. He is obviously very intelligent, having gone to college, and proves his intelligence by creating a master plan to avenge his father and taking painfully long to make any decision. Yet, he is still cowardly because he cannot muster the courage to kill himself even though he obviously doesn't want to live any longer. Another instance that he comes across as cowardly is when he won't kill Claudius while he is praying because he's afraid he will send him to heaven.