In both drama one can find: Body swap, intrigues and conspiracies. Moreover in both drama the main characters after a lot of struggle end up managing to actually help the people they love and ameliorate their life despite what their own ending is. both drama have lots of comedy yet they also contain a lot of heartwrenching moments.

Both have:
-fantasy and martial arts
-Strong, charismatic, powerful morally grey main leads
-painful pasts and misunderstandings.

Both drama are so deliciously painful.
The love! The sacrifice! The eternal suffering and romance that surpasses time and universes.

both drama have:
-Time travel/isekai
-a looooong romance plotline
-love triangle
-decisions decisions decisions
Love better than immortality is much more frustrating though

They both are time travel romance with a heavy love triangle plotline. Which at points is able to make your blood boil over the decisions and actions of the main characters. Although they deal with different eras.

Both drama deal with a time travel romance with many medical elements. Both fun and sad. Though where live up to your name is more lighthearted, faith is more melodramatic.

Both have:
-Time travel
-romance
-court power battles
-secrets
-lighthearted plot yet with painful moments

-Fun and funny time travel drama with a twist. (Although due to censorship joy of life's time travel was hidden)
-seemingly lighthearted and then the pain attacks you at random points
-secrets and plots
-interesting side character plotlines
-joy of life had more adventure than romance.

Time travel for the win. Amazing and fun main lead, secrets, plots etc. Of course nobunaga concerto focuses more on the politics while mr queen on the romance. Still they give off the same feeling.

they are both cute, fun and at times painful isekai/time travel drama with really good chemistry between the main couple

They give off the same atmosphere
Wintery themes, slow burning romance
Of course A Piece of Your Mind is more calm and toned down.

Both drama have:
-a career woman with a soft/sweet side
-a young talented Main Lead
-Societal Expectations
-Female Friendship
-Strong 2nd Lead Presence
- the topic: what truly makes you happy