Chief Inspector (2024)

Same male lead. Has same vibes just without the time travel that is in signal. Crime-solving in pre tech times

Well... one thing similar is that is a historical dramas. In "Life on Mars" the action takes place in 1988 "Chief Detective" the action will take place a little earlier in 1958.
It will take you to those times that seems close yet so far. As someone who was born in 1999 I wanted to see the world before me. These dramas are perfect way to send you back visually and emotionally.
If you want you can watch the original version of "Life on Mars"

Both are set in sort of the same time period -- minus the time travel aspect but both deal with crimes and criming solving within a certain period of time when policing wasn't so cut and dry or as cemented as it is today

Both shows involve a team dedicated to seeking justice and correcting and removing the ills in society.
Both shows involve a decent amount of action.
Male lead has a charming side in both.
Male lead (Le Je Hoon's character) in both shows have had a traumatic past experience.

They are both about crime solving but in different time period. They have a somewhat similar ML vibe with all the chaos they bring when they are investigating