They are both based on horror/psychological thriller manga, both follow the idea of a hero or group of heroes trying to uncover and catch a mastermind who wants everyone dead, and despite the similarities, the stories vary greatly in many ways. Plus, Ousama Game is one movie instead of a series, so you won't be wasting much time if you happen not to like it!
Both shows have a lot of suspense and action. The story is about a teenage boy that is involved (because of blood ties (in HTE) or by being a talented hacker (in BM)) in a struggle of law enforcement against terrorists. In both shows the protagonists gradually, step by step, find out the real intentions of the criminals and (may be) "save the world" in the end.
Both shows are psychological thrillers where the bad guys want to change a "fallen" Japan by singling out their "chosen ones." Both are more centered upon the mysterious plot than any romantic themes. Part terrorism, part friendship; the stories give a little bit of the same feel. Fallen Angel is shorter though and a little bit less in depth/drawn out.