I love both Love Never Dies and Phantom of the Opera. Love Never Dies explained more about when Christine died and who the child's real father was. In Phantom of the Opera they never clarified that. So I love how the two tie together. I wouldn't mind seeing Love Never Dies live on broadway(saw it on youtube, shows all the scenes. Look for the author LoveNeverDies if you haven't seen it).
I like them both for different reasons.
Phantom of the Opera is just classic. It's beautiful written and it flows wonderfully.
Love Never Dies is so edgy compared to Phantom. I really liked that. It was a lot darker too. The only thing I don't like is the child, but boy's voices freak me out. So high pitched.
I can't choose between them though. I love Andrew Lloyd Weber.