I've always viewed Battle Royale as a modern parable of sorts. I think it's a persuasive exploration into how people behave in extreme, life or death situations, and they applied it to 15 year olds superbly. In the book, manga, and film, they all felt real and authentic, and it was easy to connect to characters and determine which ones you wanted to see survive, and which ones you didn't. Even then, it threw in twists that made you completely question what you thought of characters i.e. Mitsuko. The romance in that actually worked as well, it wasn't forced or made the central focus, instead they developed it by having them act quite awkwardly around each other, so how young, inexperienced teenagers would probably act. The world in BR was developed poorly though, especially in the book.
As for THG, don't get me started, I got into so many arguments on IMDb

to this day, I think Suzanne Collins straddles the line between straight off plagiarising BR, the similarities between the two are unbelievable, even the sequels share uncanny resemblances to BR and BR2. I don't think it has any serious points, or if it did, they were conveyed poorly. The romance was ridiculous as well, what 16 year old makes undying proclamations of love to people? What made it worse was not one of the 3 people involved in that triangle were particularly interesting or even nice. Yeah, I'm not a fan of it whatsoever, but I will say the films are significantly better than the books, they were horrendously boring and slow.