Tons of SPOILERS:
The Good: The directing and staging was nothing short of brilliant. The set and costumes were also lovely. I particularly liked some of the Coney Island costumes though I confess I wasn't around in 1905 and don't know much about early 20th century Coney Island to know if it the depiction was even remotely accurate. I'm assuming it wasn't but it still looked pretty regardless. The orchestrations also sounded beautiful.
The scene where the Phantom takes Gustave to his dreamland was a huge hot mess. I say that as a term of endearment though as I actually enjoyed the scenes and the superfluous costumes though I had no idea what was going on.
Meg Giry is far more fleshed out than she is in The Phantom of the Opera. She has a lot of conflicting emotions about wanting to meet old friends and her own selfish desires and failure to live up her mother's expectations. Her story arc is by far the most interesting.
The Bad:
Raoul and Christine's relationship is entirely uninteresting. There's nothing about Raoul that makes me care one way or another what happens to him. In The Phantom of the Opera, we have scenes that depict him as sympathetic and loving (like when Christine looks at a picture of her father) but in Love Never Dies we see him as mostly self-absorbed husband and as a terrible, uncaring father. I'm not really sure if I'm supposed to be upset or happy about his fate and this is a serious issue with the book. The one moment that's supposed to evoke sympathy for the character (the first song of Act 2) falls largely flat because it comes out of nowhere and he doesn't really offer any solution to how to become a better husband.
I still don't understand the three "people" that are supposed to be the Phatom's cronies. It could've been interesting if they were fleshed out to be anything other than random henchmen but I'm not sure why they attempted to make characterizations of people we're never really introduced to. It comes off as just being desperate for people to talk about something. Also, since the show has incredible, gaping plot holes and moves at a snail's pace, they are mainly used as a device to get the show moving.
Gustave could be a story arc that would provide some tension but we can see almost as soon as he enters the stage that he's the Phatom's son. I'm not sure if it was supposed to be so predictable but it makes the payoff at the big scene at the end fall incredibly flat. His evolved view of the Phantom from fear to love/respect is essentially the same tired storyline we see with Christine in Phantom although the twist at the end of Phantom with Christine choosing Raoul leaves a certain degree of intrigue. The ending of Love Never Dies has none of that.
The Ugly:
The score is Webber at his worst. I actually don't hate the Phantom score like some on here do though I could never listen to it more than once in a short period of time as it is incredibly repetitive. Love Never Dies magnifies all of Webber's worst problems. There are only so many ballads we can take that all sound the same without losing interest or meaning. In Phantom, Webber tries out patience, here, he shatters it.
The lyrics are even worse. They're horribly predictable and juvenile and really are in embarrassment surrounded by such an opulent production. Insipid, sappy lyrics about hearts and choices and love and death aren't engaging or insightful. Repeated over and over again, it just becomes unbearable.
The book is perhaps even worse. Apart from the interesting arc Meg has that I described above, every other character is predictable, one-dimensional, and just boring. The Phantom had intrigue at the beginning of the show as he watched over the Coney Island dancers but by the end of all of the aura and magic of the Phantom seems to be evaporated. As many have noted, in the Phantom of the Opera, the Phantom is only on stage for a very short period of time and thus there is a tremendous amount of dramatic tension as he appears seemingly out of nowhere and has this omnipresence that haunts the Paris Opera House but also the Majestic Theatre. There's basically one uninteresting storyline - the Phantom tries to bring Christine to America. Everything else feels derivative and we know exactly how the one storyline will pan out from the very beginning.
Killing Christine should have been dramatic but it didn't really evoke any emotions. I confess I was genuinely surprised as I thought if anyone would die it would be the Phantom to really close out the show but alas Webber wants to perhaps leave room for yet another sequel. I never found her character to be particularly exciting and Love Never Dies evaporates any of the compassion we may have felt for her in the Phantom of the Opera like during the graveyard scene.
So? Overall assessment. Hated the book, the score, and the lyrics. Everything else ranged from decent to excellent but it's hard to have a good musical when the three main components of the musical are lacking. To be honest, the Phantom of the Opera, which I would rate as an average show (nowhere near deserving of everything that's happened to it but not as bad as some on here suggest) far surpasses Love Never Dies in almost every way.
Scratch and claw for every day you're worth!
Make them drag you screaming from life, keep dreaming
You'll live forever here on earth.