Both have different tribes (immortals, humans, demons). Both have a mischievous FL and a strong ML. Both have adventures on the immortal realm and on earth.

Ever since the first episode of Flex X Cop I can't stop thinking it has the same vibes as Psychopath Diary.
Both dramas are mystery dramas with a good dose of humor. Both male leads are not typical cops. In Flex X Cop the male lead is a seemingly carefree chaebol who is appointed as a police officer without undergoing proper training, while in Psychopath Diary the male lead is a civilian who (accidentally) helps the police find a serial killer. Both ML are smart (although in PD we see the ML wit only in the last few episodes). Both FL are strong and independent and both of them have a police officer father who had been involved in a difficult situation during their work (in FXC the FL father was wrongfully accused for bribery while in PD FL father had an accident that left him mentally challenged during investigating a case). Furthermore, the soundtracks of both dramas are delightful.