Detective K: Secret of Virtuous Widow

Both movies are set in ancient times, and both involve detective's who are asked by the Monarch to get to the root of a series of murders.

Detective K seems to be a ripoff of Detective Dee.
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Tonally different but plenty of similar details like Christian persecution, king's tribute, murders, and more. One has a darker, serious tone till the very end, while the other include flashes of comedic reliefs and a light-hearted hopeful feeling towards the end.

Both are comedies set in the Joseon era, showcasing a funny investigative duo trying to solve mysterious cases.