Both are based from a novel by Fumie Kondo. Judging from the first few episodes of both dramas, they are similar with some details. Aside from the mystery thriller vibe from both, a high school backstory is a common ground. In addition, the female protagonists are both writers. In Influence, Oikawa Tomomi is a novelist while Makabe Suzune is a scriptwriter.
In Influence, the second female lead took the blame of the first male lead for murdering a man for self defense to save her friend. So the second female lead went to juvenile. in the Innocent man, the male lead took the blame of the female lead - his girlfriend for murdering a man by self defense. So the male lead went to jail.