Both focus around law and lawyers. Both feature an "obviously bad guy" character who keeps evading the law and the main characters. Both deal with how there are loop holes in law and how it can be hard to deal with law when you have emotional attachments to the suit in progress.

(and also Seven Days: Friday-Sunday which is part 2)

both are about boys finding romantic feelings for each other and both have a fairly chill and light-hearted vibe about it. They also both have a sort of similar ending where there is a separation through a misunderstanding and then a reconnection.

One is Korean and one is Japanese though, so up to you if that bothers you.

Both feature a female lead who is very dramatic and over the top and a little bit silly.
Both feature a male lead who is just your average good-hearted dude who happens to have a special magical power that can help the female lead do her job.
Both feature the idea of the mystical world just beyond what most people can see and are about helping people.
Both have serious moments among lighthearted levity.

A similar setup for the plot! A woman from the past with a tragic backstory who is immortal/dead must grant wishes/put people at ease in order to fulfill her duty and pass on peacefully. She does it with the help of the main male lead who gets thrown into it all. She is tough, surly, and just SO done. Pop-up bar seems to be a little bit more comedic than hotel so far.

Both movies deal with a character who was kidnapped at a young age and dealing with the trauma of that and how to move on and heal. Also they both don’t like being touched and have nightmares as a result of their trauma. Also both have a trigger warning for suicide/an attempt/references.

Same female lead actress.
The dynamic between the two leads is sort of similar. Start off at odds (he seems stuck up) but grow to know each other.
Office romance.
The male leads both had something traumatic happen to them in the past.
Both male lead characters actually KNEW the female lead as a kid but the female lead forgot about it.

Both have Kim Jaewook as one of the main leads where their character is a PRO at their particular field. Also both use a filming style of having hyper stylized scenes, often where a character is imaging things/day dreaming. Antique is a little bit darker in theme/topic but both have light hearted moments and have characters who learn to open up to others and trust a bit, especially when it comes to confronting their past and their traumas. OH! and they are both fairly LGTBQ+ positive. In Antique there is a gay main character and in Her Private Life there is a situation in which a character is misunderstood as being in a gay relationship and the main character is supportive about it and even though they laugh about it later its never looked down on!

Similar premise, souls seperated by time and by past tragic events. Dealing with the idea of healing and moving on to the next reincarnation. Ghosts and magic!

Both are a mix of romance and drama, the romance of this show being separated by time travel (very similar to W's two world separation).