Both dramas have incredibly intelligent psychopathic serial killers (especially Gap Dong).
If you enjoy those kind of stories you will definitely like both of these dramas.
While Hello Monster has a really complex story with incredibly diverse characters, Gap Dong's story is way darker and focuses more on the nature and the perspective of the serial killer and his actions.

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In my opinion the actors for Hello Monster were all incredibly well cast which helped to improve the story and made it easier to portray the characters. In contrary for Gap Dong Lee Joon did an amazing job on portraying a coldhearted psychopathic killer, while in my opinion the other main roles were poorly cast/ badly portrayed, which didn't really help the storyline...

Both deal with North-Korea and South-Korea and show the conflict of the two countries.
While Confidential Assignment has a North and a South-Korean Cop cooperating and shows a bit of the South Korean perspective of North Korea; Secretly, Greatly deals with North-Korean Soldiers and Spies undercover in South Korea.
Both movies have amazing action scenes, a great story and are also really funny.

In both dramas the main protagonist/group are solving new interesting cases each episode.
If you like the concept and the crime genre you will definitely like both.

In Vampire Prosecutor it's a well Prosecutor who is a Vampire.
In God's Quiz the main character is a "normal" intelligent doctor, who helps solving many cases.