I really don't think that Battle Royale and the Hunger Games are all that similar. What is there besides the premise of children killing each other as part of a government policy?
If Suzanne Collins ripped off any work of fiction, it would be Surviving Antarctica: Reality TV 2083.
The relatively obscure young adult novel (released in 2006, a full two years before the Hunger Games) is set in a practically identical world. Both novels take place in a dystopian North America, in which the decadent government rules its impoverished through force and propaganda. Very similar to the principal of the Reaping, all fourteen year olds must undergo "the toss", in which a simple role of the dice determines if they'll be forced to live in poverty or enjoy the luxury of the ruling class.
Well, a group of teenagers (unlike the Hunger Games, these children are volunteers who are being paid) are sent to explore Antarctica alone, reenacting the trip made by Robert Scott nearly two centuries prior. Much like in Collins' novel, the entire affair is shown on television to an audience, and is a major annual event. Although this wasn't present in the book, the film of the Hunger Games and Surviving Antarctica both spend ample time following a young man who helps shape the games each year, who ultimately rebels against the government by breaking the rules to keep some of the children alive and appease the destitute audience.
The similarities aren't only in the plot. In the 2008 novel and the film, the Capitol's citizens are described and shown as having lavish and garish fashion styles. Several characters in Surviving Antarctica have ridiculously colored hair or skin, and one unnamed woman's locks end at her ankles. President Coin, a major character in Mockingjay, is very similar to the US President introduced at the end of Surviving Antarctica.
Much like with Battle Royale, however, the Hunger Games delves far more deeply into the themes and concepts of Surviving Antarctica, and ultimately proves itself to be the better novel.