Burton is not afraid to make cuts and changes to make Stephen Sondheim's original stage show (which already is available on DVD for those who are curious) a more cinematic experience.
Be that as it may, I had actually seen the musical prior to seeing the movie and I was actually surprised how faithful it was. I was expecting some form of artistic license to be taken and have bits and pieces of the story altered slightly, but surprisingly it was all essentially intact, from the beginning right up to the conclusion.