The reason peter pan 2003 is so good is because it's like the only iteration to actually grapple with the themes and subtext and nuance of the material in the way that it does.
Because yes, it is frightening to be Wendy Darling. — A young girl starting to become a young woman and suddenly, instead of playing with her brothers and telling fantastical, gruesome stories the grown ups start telling her its time to grow up. to put away her childish things and move out of her beloved nursery. saying dreadful, confusing things about her having a "hidden kiss" and "finding the person it belongs to" and "no, no, don't be afraid, that's actually the greatest adventure of all, you see?"
And yes, Peter Pan — the boy who doesn't grow up — is wondrous and magical and free-spirited and charming, but he's also tragic. He visits the girl, this Wendy, who tells wonderful stories of adventure (stories about true love and happily ever afters) and he whisks her away to Neverland so she'll never have to grow up as well — he even takes those pesky brothers of hers that he doesn't care about, at her request — and then immediately begins casting the two of them in "make-believe" grown up roles. He is "father" and she is "mother." He has the lost boys build her a house. He dances with her just as the Fairy King dances with the Fairy Queen. The idea of her leaving to grow old, having a husband, someone who is not him, angers and upsets him, and yet he's just as terrified to confront those feelings. He's what Wendy is — a child afraid of growing up — but instead of finally being able to accept the bad that comes adulthood in order to get the good — like Wendy comes to do — he chooses to remain as he is, and thus is always longing for something just beyond him.
And then of course, there's Hook, this third character that plays such an... interesting role to the two of them resepctively? To Wendy, he's someone who is abhorrent and yet also strangely enthralling. In order to get to Pan, Hook manipulates Wendy, and of course that means flattery and smooth-talking and taking her oh-so-seriously and Wendy is once again contending with the fact that hey maybe growing up does have some merits. (The actor for him is also the same actor for Mr. Darling, and yes that is intentional). And then for Peter... well actually, the dynamic is more like what Peter is to Hook because Hook is obsessed with Peter Pan. Peter is Hook's villain. The sole focus of every waking thought. But for Peter, Hook's sort of there whenever Peter's ready for another adventure. For a fun battle. For mindless torment. He does not think about Hook the way Hook does about him (at least not to the same degree) and it's honestly kind of pitiful for Hook? Like when Peter first shows up with Wendy, this actually sends Hook spiraling into this bizarre sort of jealousy. "If Peter has Wendy, where does that leave me?" And yet, there is still this distorted mirror between the two of them. That Hook is something Peter fears becoming. Old, alone, and forgotten about.
And then just the general atmosphere of the movie... It doesn't shy away from the darker aspects and implications of fairy-tales and magic. Multiple people die on-screen. Hook commonly kills his crew when aggravated. Tinker Bell manipulates the lost boys into shooting Wendy with an arrow, and Peter almost kills one of the Lost Boys in retaliation before realizing Wendy isn't dead (and the dialogue here to me implies Peter has killed lost boys before). The mermaids are just as eery as they are beautiful. Peter warns Wendy that they'll "sweetly drown you if you get too close" — which they almost do to Wendy, sort of enchanting/beguiling her into the water before Peter pulls her away, and yet it doesn't feel entirely dissimilar to how Peter sweetly convinced Wendy to leave her world behind and come with him.