Okay, this is where I can start talking about the meat of the film, and where a lot of controversy has come in some circles. I'm going to start by stating that, without doubt, Wendy is the protagonist of the story, not Peter. So much so that "Wendy and Peter Pan" would technically be a better title, at least in the sense that it would represent who gets more plot and character relevance. Now, there's an argument to be made that Wendy is indeed the true protagonist of the Peter Pan story (certainly she's always been more important than Michael and John, who like their other incarnations are without any real presence or plot relevance), but there's no grey area here - Wendy IS the protagonist. It's Wendy who has the character arc, it's Wendy from whom we see most of the film's events, it's Wendy for whom the themes are most clearly reflected.
And y'know what? I'm fine with that. We can debate how loyal this is to the original work, but Wendy here is a solid character (fun fact: she's played by the daughter of Paul Anderson and Mila Jovovich, and I first saw her in Resident Evil: The Final Chapter) with good acting chops behind her. I'm not going to go step by step, but basically, she carries the movie.
Concerning Peter, I've seen a lot of people complaining about him for various reasons, among them that Peter is a "villain" in this movie. And...look, I know a lot of media is subjective, people are free to draw their own conclusions provided they're supported by the text, but if you read Peter Pan and think Peter is a standup hero, no questions asked, then I'm sorry, I just don't see how you can come to that conclusion. If you've only watched stuff like the 1950s Disney movie or the 2010s Pan movie, then sure, but to claim that Peter's 'villany' is a betrayal of the character indicates to me that you don't understand the type of person Peter is, at least by my reading. It's not right to say that Peter is "evil," but my understanding of Peter is something akin to a fae trickster. Amoral, because as a perpetual child, his moral core isn't developed enough to weigh the impacts of his actions.
At the least, that's how this film goes with things. Peter here is capricious, arrogant, etc. It's revealed that James Hook (originally called "James") was a lost boy. The FIRST lost boy, but Peter forced him to leave Neverland when he (James) started asking about his mother. Peter's original accounting of events is that "I'm the good guy, he's the bad guy, we fight," and even Wendy points out that there has to be more to the story than that. Peter certainly has a character arc in this movie, but it's an arc that I'd say remains true to the character. He grows up enough to apologize to Hook, to let the Darlings and Lost Boys leave, but he himself stays in Neverland, as there's no going home for him. It turns out that Wendy's house used to be Peter's, but his mother is long gone, so for him, he's stuck as is.
Concerning Hook, well, I've already summarized a lot of his character here, but regardless, it's a sound one. Jude Law conveys both menace, humour, and sympathy. This is a man who's quite happy in executing his own men as well as children, but is clearly a wounded soul. A man who's the result of Peter's actions and his own. Again, none of that is groundbreaking in terms of character concepts, but it does give Hook more depth than, well, probably any Peter Pan story I've seen (sans possibly Pan, but that was doing its own thing). Anyway, Hook is great in this.
Who else is there? Well, John and Michael are non-entities, but what else is new? The Lost Boys (and girls, because reasons) are fine. Tinkerbell is...alright, I'll be honest, I've never really understood why Tinkerbell of all characters got so much attention over the years. In the 1950s film, she's a jealous twat that barely has any character. In Pan, she appears for a few minutes. In the original book, she barely does anything. Yet this fairy got her own sub-series because...reasons. Meh, whatever, Tinkerbell here is decent enough. She speaks by 'jingling' through the entire film and Wendy can't understand her. Peter claims that he can, and 'translates' for her, but it's revealed that this is B.S., and Peter's saying whatever he wants Tinkerbell to have said, so to speak, yet it's Wendy who, at the end, is able to understand her. As Tinkerbell whispers (paraphrased) "thank you for being able to listen to me/understand me." Again, nothing major, but it's decent enough.
And rounding things up, Tiger Lily. Weird thing about Tiger Lily is that she's been more, ugh, "empowered" as time goes on. I can't even remember what she does in the original book sans be kidnapped, the 1950s film isn't much better, Pan sets her up as a warrior with a Peter-Hook love triangle sort of hinted, this film kind of splits the difference. The Tiger Lily here does fight in the final battle, but her main contribution is saving Peter after he's fatally wounded by Hook earlier in the movie. There's a sense of disconnect between Tiger Lily and the Lost Boys - for instance, she can't go into the Lost Boys hideout, and it's implied (least from what I recall) is that there's a fundamental difference between her and the Lost Boys. The idea that she's native to Neverland, while they're fundamentally 'wrong,' in the sense that their growth has been retarted. Because clearly Tiger Lily and her tribe seem to age normally, while the Lost Boys don't. Of course, I may be reading too much into this, but I'd say that like most of the characters here, this is the best take on the character I've seen in an adaptation.