Both leads are adults that get trapped as high schoolers again, have a mission of saving someone that is suffering and making their lives happier, and then falling in love in the process. Overall same vibes in terms of how they approach fluff and humor. Even the SML personalities kinda resemble each other. Probably way more I'm missing here but they have so much in common!

Premises are very similar! Both have a FL that's in high school and is really smart but dealing w bullying, absent parents, and financial struggles. FL in both find help/comfort in a guy who is otherwise an outcast and looked down on in society.

Sound of Magic doesn't really have romance while Better Days kinda does, but they tackle the same social issues.

They’re both historical dramas where the FL’s soul has been swapped. There’s a similar setup where the FL is surrounded by several male characters that grow fond of her, all from royal families.

Both are fantasy historical dramas where one person's soul ends up in another person's body. They follow the premise of the FL trying to get out of the body they've ended up in, but Alchemy of Souls has more magical elements while Mr. Queen is around time travel. I also think they have a similar type of humor where it shouldn't be taken too seriously even when the drama's setting deals with intense stuff like royalty and politics.

They both deal with similar psychological themes (e.g., trauma, othering) and have an element of fantasy. Visually they're similar as well with the colors, cinematography, butterfly theme, and even the style of animation in the opening title sequence.

Both are character-driven and have a found family type of vibe where people who are lonely and misunderstood find comfort in each other. Overall they're dark, but they present important messages with an optimistic outlook.

Both dramas focus on two guys that have different lifestyles and a considerable age gap but are forced to learn to get along with each other. They are heartwarming slice of life dramas with similar mood/pacing and make you think about and appreciate the little things in life.