In both of these series, an innocent person is forced into the position of a serial killer, in Tengoku to Jigoku it's through body-swapping, and in Psychopath Diary it's through amnesia. They also both include police investigation and a bit of mystery.
Both have a character that's an outsider arriving at a place that holds secrets. Both are thrillers with mystery and psychological elements. Both have unsettling characters.
Both are light, easy to watch dramas. They both have people teaming up to do detective work in ancient times.