Battle Royale is about a game that is set in Tokyo in the future. In the new government system, there is a new TV show called "The Program". The Program consists of a random ninth grade class battling it out on a barren island where its inhabitants have all been evacuated. The students are supposed to kill each other until one survives. There is no way for anyone to leave the island, and if there isn't a winner after three days, everyone dies. Wonderful, yes?
Saikano (full name : Saishu-Heiki Kanojo or in English She, The Ultimate Weapon) is about a couple (

) who first started going out because the female was dared to do it since she liked a certain boy. Eventually they grew to love each other, but the girl, Chise, had a problem. One day, Chise's boyfriend, Shuji was hanging out in a mall with his friends, until there was an air raid. One of his friends dies, and Shuji see Chise in a different form. When Shuji see this Chise explains to him that she is a weapon on mass destruction used by the army. Basically from that, the show continues on about their relationship and Chise's military problem. The show is very depressing, and as far as I have heard it is as depressing as the Cowboy Bebop Anime (not the movie) ending, if not it is more depressing.
Hope that cleared up some stuff.