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.

Both dramas have as their story a group of people who conduct human experiments. In both dramas people escaped their facility and developed superpowers. In Luca and in Awake those children, which were experimented on, hold the key to the success for this experiment and are therefore wanted and hunted.
Truly it feels like the exact same story just different characters.

Although revolves around the military and another around prison both dramas are very similar regarding the relationship between the male leads and their respective girlfriends. Especially the story of Seo Dae Yeong x Yoon Myung Ju (DOTS) and Kim Je Hyuk x Kim Ji Ho (Prison Playbook) is very very similar.

Evil spirits. People with a special ability that fight against them, teaming up with someone from the law enforcement.
The Cursed is like the horror version of The Uncanny Counter.

Both are crime dramas that debate the morals behind of ones personal justice. Both deal about characters that change due to things that have happened to them. Both are absolutely mind blowing in terms of character complexity, story development and cases. Absolutely unforgettable experience.

+ Both dramas are extremely well connected crime dramas where the cases are linked to the characters on a personal level.
+ both thematize the psychological aspect => While in Signal the psychological aspect is more debated and analyses, in Burning Ice you can really see psychological methods being used.
+ Both dramas show very well character development.
+ both are connected to past events

If you enjoy the cases in Signal you are bound to enjoy Burning Ice.

Both dramas deal about girls that are getting bullied and have something happen to them because of this. In both dramas family members take revenge and things become very fast very extreme.

Perfect World is the romanticized version of Josee, and Josee the brutal reality of Perfect World.
While Josee deals about a girl who is handicapped, Perfect World deals about a guy who is in a similar situation. Both dramas deal about the perceptions of being disabled and also about what this means for the family, their love life and the people themselves.

Poor husband, wife's dreams broken => leads to divorce. Then after years of separation both meet again. Both males are now successful while their ex-wives are not having much work out for them. And the drama begins.