Both directed by Lee Byeong-heon.
Both starring Ryu Seung-ryong as main character running fried chicken joint.
Both contains mystery and comedy.

Hwang Jung-min masterclass.
Noir crime thrillers.
Corruption.
Cops vs organized crime in New World, Cops vs corrupt mayor in Asura.

I want to make a correction to the below recommendation that Chicago Typewriter is NOT set during the Joseon period, but during Korea under Japanese rule, while Mr. Sunshine is set right before that, during the brief awkward period between Joseon and Japanese rule (called the Korean Empire 1897-1910).

Prequel and sequel, and both starring Hu Ge as the main lead. Both are considered classics in chinese dramas.

Slow burn art films. Creates romance not out of overt displays of affection but rather through implication and omission.

Lee Young Ae's comeback drama after 14 years. One drama tells the story of the first female royal physician in Korean history, the other about a Korean artist, writer, calligraphist, and poet who is also the mother of a Confucian scholar.

Political thriller drama films taking place in 1979. One is based on the assassination of president Park Chung Hee in October 26, while the other is based on the Coup d'etat led by Chun Doo Hwan on December 12 in the same year, just a few months later.

A Time Called You is a korean remake of Someday or One Day. The same year, 1998, is also used for the past.

Both involves the main character as an undercover cop infiltrating a crime syndicate. Difficult situation of preventing identity from getting exposed.

Both involve a psychopath serial killer. Cops that are extremely frustrating and incompetent at their job that it becomes almost laughable.

Disaster movies starring Lee Byung Hun. One is about airplane terrorism while the other is about a volcanic eruption.

Kang Ha Neul and Jung So Min reunion. Both also played love interests.
Both are romantic comedy movies.