Both had:
-similar vibes
-bullying
-murder
-protective male lead
-independent FL
-harsh topic

Differences:

My Name:
-K-drama
-Fl was a part of a gang
-FL was a double agent (police officer/gang member)
-ML was a detective
-Adult life

Better Days:
-Criminals
-More of high school
- A lot more romance

In both dramas:
- Both dramas revolve around royals
- The FL has great martial arts skills, military tactics, and schemes
- The FL is naughty and acts freely, never afraid to speak their mind
- A prince from the grasslands took interest in the FL
- The main leads had complicated relationships
- The ML is an orphan/ adopted into a different place
- The main leads had many admirers
- The supports lead pairs up