Both crimes are due to religious fanatics/cults. In both the police are smart and have ties from their youths.
Both take place in an office setting and about in-office politics. It also contains wire-tapping and the tapper growing to respect/like the tappee due to listening and learning about their true selves. It also becomes like an obsession for them to listen in on the person's life. Chief Kim is a more lighter drama with some heavy themes, where in My Mister is a heavier with some light scenes.