Lou

Both dramas have a couple that is meeting due to unusual circumstance again but where one of them makes the decision to help the other. By doing so all actors get involved in a case that challenges not only the relationship they have, but also the characters development too.
There are a lot more similarities between them however naming them would spoiler too much.
IF you enjoy one there is a high chance you will enjoy the other drama too.

Both were released nearly at the same time and both are absolutely gripping dramas that will leave you guessing on what happened and who is responsible for it.
Both have absolutely amazing cinematography and background ist, astonishing acting and interesting characters that are so diverse and complex.

The only difference is that while Burning Ice focuses on one specific case with multiple parties involved, Day and Night focuses more on a variety of cases.

Nonetheless there is a high chance that if you like one you will enjoy the other drama.

Both are crime dramas where the leader of the investigation team is a woman. Both women are very smart and skilled to find the culprits of the cases they handle. Both women are challenged by the work and family situation.
Both give off a very similar feeling.

Both dramas revolve around a character who gets confronted with the death of a close family member. In both dramas the character seems to be the one behind that murder. Throughout the drama we learn what has happened. Both dramas have characters that have amnesia and slowly throughout the drama get their memories back.
Both are gripping crime dramas that will keep you on your seat.

Beyond Evil and CHIP-IN both start with cases where a group of people could be the culprit. In CHIP-IN the focus lays on the righteous daughter, in Beyond Evil it starts with the righteous new detective. Both team up with someone who they are suspicious off but still work together with.
Throwing around theories and questioning and suspecting everyone at one specific point makes both dramas not only darn gripping but also makes them very similar to one another.

Both dramas deal about a case that has happened long ago but is linked to the protagonists. In both dramas we have a male duo where both are at one point accused of the crime. Both have strong female characters and both are nail biting and make you stay glued onto your seat.

Both are crime/Investigation dramas that revolve around a investigation team. Both use psychological aspects in order to discover the murderer. Both have a team set up with a female who holds a special role. In both dramas a partnership is established between the female lead and the male lead. The Listener has however a smarter female lead.

Both dramas deal around a character that seems to be neither good or bad. While the viewer is left to question if the main character is the hero or the villain that everyone is looking for. Both dramas show a team where all characters have a difficult childhood and in both dramas characters are closely watched due to their fathers being criminals.

What is the trigger for a person to change their persona and become the next criminal? this question is debated in both dramas. Both are very well developed crime/thrillers, with controversial topics. Both show that the innocent children must not always be innocent and both show psychopathic behavior to the extreme.
There is a high chance that if you like one drama, that you will enjoy the other as well.

Both are absolutely mind-blowing crime/thriller dramas with an extremely well connected storyline, controversial topics and gripping characters. Both deal around the psychological aspect of victims and murders.
Analyzing the mind of people.
Finding out what triggers who.
Psychopaths and "innocent people" becoming monsters.
These are all aspects found in both dramas.
"Burning Ice" is a tad bit more well developed but "Mouse" is definitely more extreme to watch.

Begin Again has a different start - the girl is rich, and starts a contract marriage with the guy, while Autumns Concerto follows two late teens where he is the rich boy. Something happens and both couples separate but meet again after a few years. The story that follows afterwards is very very similar to each drama, due to spoilers I cannot reveal more.
But if you like one you might also enjoy the other drama.

Both dramas have Hyun Bin as a lead who plays a north korean who is in the military and comes to south korea for a mission. During his partners up with a south korean detective and lives with his family.
The concept is very similar but Crash Landing is the romantic/humor version whereas Confidential Assignment is full with action and has nearly zero romance.