I think Battle Royale was a much better read than Hunger Games. I haven't seen either of the movies.
I got about 100 pages into the third Hunger Games book and I just couldn't take it anymore. It was clear from the beginning that the author was writing for a teenage audience, but I knew that going into it. Still, it was readable enough until the third book when I just couldn't stomach how seriously the author was taking it all, despite the premise being completely absurd and the characters not being written very believably.
What I liked about Battle Royale is that, although it was also a completely absurd premise and no doubt the author also took his work seriously, it came off to me as over-the-top enough to just be enjoyable for enjoyment's sake.
It might just be how I allowed myself to perceive the two stories that made the difference in how I liked them. I liked Hunger Games enough until the third book. I looked at Hunger Games as having more of an agenda, even if that's not necessarily true, and I saw Battle Royale as just being a fun action story as long as it wasn't taken too seriously.
I guess I'm not surprised at how popular Hunger Games has become considering its target audience. I heard people say it's going to be even better than the Twilight series!
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"Filthy lawbreaker, unhand that vending machine!" - Casey Jones