My Friend Dahmer comes at the story of Jeffery Dahmer from an interesting angle it follows Dahmer growing up at school, following from aged 17 to his first murder at 18 - the film stops just after he picks up Steven Hicks. However, when I was watching this movie, I was thinking of a less violent but just as emotionally wringing version of the brilliant Henry: Portrait of a Serial Killer, based heavily on Henry Lee Lucas.
The true life serial killer genre isn't exactly over-crowded, just more that there's fictionalised ones that take more of a forefront - Hannibal Lecter, Norman Bates, Freddy Krueger all for instance - and they always portray those characters with a certain degree of appeal.