This book is often mentioned alongside other classics of the dystopic genre, so I'm naturally drawn to compare.
Contrasted with the biggest one, Hunger Games, I'd say the biggest difference is the depth of world-building. In Hunger Games a lot of time is spent establishing the characters and the world they inhabit. While the same is also present in Battle Royale, it's much narrower in scope, with most of the time being spent looking over the shoulders and into the minds of the various students. (Compared to Hunger Games, which - if I recall correctly - only had a single PoV character.)
The other comparison at hand would be to Orwell's 1984, which is often mentioned alongside Huxley's Brave New World. When I started reading Battle Royale, for some reason I expected something more along the lines of those two, so I've been surprised when it turned out so action-packed.
I definitely see strong similarities with 1984; it, too, depicts a successful totalitarian regime that keeps its citizens in check with brutal efficiency, even though the methods differ.
If 1984's ruling class uses the stick more than anything else, citizens of the Brave New World mostly get the carrot (and, of course, a metric ton of brainwashing). In this regard, Battle Royale falls somewhere in between - a ruthlessly efficient and cruel system, which also gives its citizens some leeway, to appease them and to make them reluctant to rebel. (But these topics are again less developed here than in 1984 or BNW.)
I'm giving it 5 stars, because I ended up liking it more than I expected. However, if you haven't read the Hunger Games trilogy yet, perhaps it would be better to start there. I think it's better tailored for the sensibilities of a modern YA reader.