This is such a great novel/musical! The main conflicts of man vs. man in this work are:
1. The phantom vs. the directors of the opera. The phantom has long given his orders to the directors to run the opera as he wanted. When new directors come to the scene, things get a little harried and the new directors bristle at being told what to do. When they don't follow his rules/orders to the "t", bad things begin happening.
2. Rauol vs. the Angel of Music (who is really the phantom/Erik). Both of these men are in love with Christine, and the phantom who has led Christine to believe he is really the Angel of Music her father said would always watch over and protect her, is not willing to just allow Rauol onto the scene to ride off into the sunset with his prize.
3. Christine vs. Erik (the phantom). When Christine is taken by the phantom to his underground hideout, Rauol comes to rescue her. The hideout is rife with hidden traps, and Rauol falls into one. Christine is forced to push a button to kill Rauol and choose Erik, or to choose Rauol and essentially kill Erik. She cares for Erik but is scared of him. She truly loves Rauol, and he is her choice.
Also, one might consider the symbolic nature of the characters "Phantom" and "Rauol". Christine is a young women in Paris at a time when women were forced into traditional roles. I see the conflict in Christine as one personified in the two male characters in her life. The Phantom represents the artistic, creative, career path a woman often wishes to pursue. Rauol represents the traditional wife, and ultimately, family/mother role she would like to pursue as well. For a woman, it is often very difficulty to balance these two roles and feel she can adequately choose between the two. Forced with chosing between marriage and a traditional life that Rauol offers and a life of creative, professional career as a famed singer/artist, Christine is torn. Many women are still faced with that choice as a dilema today....the pull between two options is often excruciating. To have to chose is not easy.