If we fast forward to the end of the film we find out that Daniels is actually a patient on the island and that he was actually in a role play that was set up by the islands doctors, in an attempt to get him to come back to reality. This is where we see who Edward Daniels truly is, a completely unbalanced hero whom denies that he is actually Andrew Laeddis, an arsonist who was convicted of killing a woman in one of the fires he created. In order to fully understand Andrew Laeddis, a second viewing is required. In his mind he has been set up by the island's institution and that he is an innocent human being who has been wrongly convicted. This is where the viewer sees the sickness that is contained within Andrew's mind. He creates fantasy situations where he can make up a reason for the way things are and then blame it on the directors of the island. He wants to believe that he is a U.S Marshall and so he creates a situation where that is true, and he doesn't see it any other way.
The journey that Andrew Laeddis undergoes could be considered one of two different ones; either a quest for identity or a quest for knowledge. The way Laeddis sees it he is searching for knowledge about the island's institution and what is really going on the island. In reality, the role play was set up by the islands overseers in attempt to get him to snap out of his dreamworld and back into reality. When Laeddis finds out who he truly is, the audience expects him to be able live in reality now that he has been exposed to the truth. The next day he is back to his schemes where he pretends that he is an U.S Marshall and he is investigating a crime on the island. As he is taken to become lobotomized after the island's directors feel he has no chance of becoming sane, he utters the question "Is it worse to live as a monster, or die as a good man?"
This question is a powerful one as every viewer in the theater was left to ponder that as the lights slowly came on and the credits began rolling. Andrew Laeddis chose the second option, as he ended up dying as Edward Daniels, at least in his mind. This question has been asked in various forms from different movies (the Dark Knight for example) and it seems that there is no definitive answer, as people's point of view will always change that answer.