The Hunger Games is not about watching kids killing each other. It's not. The movies are about the games in that the central conflict revolves around it, the characters' actions are done in the name of it. However, the actual games themselves are treated like some awful disaster that's slowly approaching closer and closer, and it will return again and again unless something is done to stop it because every time it comes soooo many people die. This is not Battle Royale. But if I had to compare them, I would do so like this:
Battle Royale is clearly intended for mature audiences only, whereas Hunger Games has a wider audience by including younger folk.
The premise is the same (Theseus and the Minotaur), but the thesis of both plots, what each story is trying to accomplish, are completely different.
The characters within the Battle Royale are all that matter which is why the movie is completely focused on the individual killing of each. The characters who play in the Hunger Games share as much plot importance as the characters outside the games, each of their actions in and outside the games are just as important to the plot, which is why so many kills happen offscreen or too quickly instead of lingering on every bloody death.
The existence of both does not determine that one is a worse version of the other (if you want to be technical, they're both ripoffs).
If you have to make a choice of which one is "objectively" better, choose Battle Royale. Both movies are entirely enjoyable, the Hunger Games wins out for me simply because I prefer drama over gruesome violence.