They are both character driver rather than plot driven. The characters in both dramas are tortured, conflicted, flawed, and complicated. Also, both dramas have a slow pace with beautiful cinematography and beautiful music although I would say A Piece of Your Mind has a far superior cinematography.

Very similar in terms of fantasy elements and conflicts. Similar love story. The chemistry between Shin Min Ah and Lee Joon Gi is great.

Both deal with a FL that suffers from bullying at school. In Better days, the ML is around the same age as the FL. Better Days is much darker and grittier in tone though.

The movie deals with school bullying and physical abuse in a darker way. It gets pretty dark and bloody towards the end.