This article is about the books only!
First thing I should say is that I really enjoyed both books.
Now, I've heard a lot and read a lot from Battle Royale fans about The Hunger Games stealing the story of their beloved book. Yes, both are stories about horrible governments forcing its teenagers/youth to fight to the death every year until (usually) one winner is declared. The evil government then gives the winner some stuff, takes pictures of them and sends them on their way to live with the consequences of the game for the rest of their lives. (I'm going to refer to the fights to the death as 'games' for both books, even though in Battle Royale it's called the 'program'). Also, yes, both lead characters have love interests, and both books feature 3 main kid characters. But that's pretty much the end of the similarities. These may seem like a lot of shared story characteristics, but I'm pretty sure the ENTIRE idea of an arena game where people fight to the death was invented by a small tribe called the Romans a really long time ago. So that concept isn't really new, but the details are, and it's the details that matter. And the details are what make these two stories completely different.
The biggest differences when reading the books is that BR is told from the perspective of different students, depending on the chapter, kind of like Game of Thrones except not as rigid in it's execution. So Shuya may be the main character, but the novel delves into the thoughts, actions, and memories of almost all 42 students participating in the game. Also, Shuya is a boy, and the main character of HG is the girl, Katniss. The entirety of HG is told from Katniss's perspective. All the memories and flashbacks are hers, and the only action the reader gets to experience during the game is what she comes across.
Another major difference between these two stories is the psychology of how the actual game is played. In BR, the students who are forced to play have no idea they have been chosen until they wake up on the island where the game will take place. Their school bus was gassed, and they've been fitted with metal collars that function as tracking devices, microphones, and bombs, which allows the government to monitor their location and their plans, and to control their behavior by being able to blow their heads off. The students are told the rules, given a pack with some food and a weapon, and the game begins. These kids, some of whom are now carrying guns, have to face the idea of killing or being killed by classmates, people they have known for a while and sometimes for years. Most of them are consumed by fear and have no idea what to do.
In HG, a boy and a girl from each of the 12 districts in Panem (post-apocalyptic USA) are selected in a lottery. They are sent off to practice for a week or so, learn some new skills, observe the other participants, and then they are sent to the game site. These kids are ready to fight and have planned their strategies for winning. They are also constantly on camera and being watched, because the entire game is a reality TV show. So not only do they have to survive in the woods (no supplies are directly given to them—and NO guns) and survive being killed by some other kids who they don't really know, they also have to try and win the sympathies of the viewers at home. The more the audience likes them, the more likely they are to receive gifts to help them in their quest for survival. The way the government monitors and controls the game here is that besides the TV cameras, they have complete control of the 'natural' environment the games take place in, they can start a fire or a storm if they think it will 'improve' the game.
The stories also differ in the reasons the games exist in the first place. In BR, Japan is part of some Greater East Asian country run as a strict dictatorship. The games are not televised and no one knows what happens during them, only that it's a fight to the death and there is one winner. The government holds these games to promote fear. To frighten its people against coming together. The games tell the citizens that they can't trust each other. In HG the games are held to entertain their loyal population in the Capitol, and to remind the poor unfortunate people in the districts that the government controls them. Of course, in the HG series as a whole, this ends up backfiring and igniting a massive revolution...but that's kind of a spoiler I guess.
Basically, BR has the psychology of Lord of the Flies, and HG has the setting of it. What I mean is, BR is horribly violent and sometimes shocking where kids who used to be friends kill each other, but the addition of guns and an environment that is normally a civilized village, make it feel more like an urban street fight. HG doesn't have that level of savage behavior and brutality, but it does take place in an environment that requires it's participants to be survivalists, ie find ways to feed themselves and build shelter.
So, should Battle Royale fans and The Hunger Games fans shit on each other on the interwebs? No.
Should BR fans read The Hunger Games or go see the movie when it comes out? Only if they want to.
Should HG fans read or watch Battle Royale? Again, only if they want to.
After reading both books and noticing how different the stories are, it is obvious that people who like one story may not enjoy the other. But personally, I really really liked them both.
The lesson here is that I should read The Running Man.
UPDATE
Multipass reviews BATTLE ROYALE the movie.
Multipass reviews THE HUNGER GAMES the movie.