Battle Royale has been touted by many as the main influence behind The Hunger Games. The author refutes this idea and states she had never seen Battle Royale before authoring the series of books. While the similarities are abundant, BR is a more stripped down tale of teen aggression that doesn't spend much time on character development. This is where The Hunger Games trumps BR as the better film.
Battle Royale is a violent film that never side steps it's goal of shocking the viewer with brutal scenes of gore and total disrespect for human life. But, it's still a fun movie that has made an apparent impression on modern film with a current theme that is now being repeated in The Hunger Games.
If you've never seen Battle Royale, I would give it a shot. This blu-ray video and audio transfers have been given the care they deserve and it's an entertaining movie.
Battle Royale II is nowhere near as good.