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both have good female characters who have a second chance and build the life they wanted

Same concept of the alien going into a dying man's body and falling in love with the woman.

They have a lot of the same feels. There is also the forbidden romance/secret identity thing going on. Cruel City is a bit darker than Healer.

young students in both films guide their teachers to a new life.

Although from two different countries, the feel is much the same; both crime mysteries that involve geniuses and a hint of romance. God's Quiz is more medical and main character mystery based, but they both have that amazing plot intrigue and touch of romance (though Subete ga F ni naru's romance feels a bit deeper over the course of the show). If you liked one you'll def. like the other :)

They are both adapted from shojo manga and about a normal girl who's pursued by the most handsome guy of the school.

In both series, the main character travels in time from the modern era to the Sengoku period and joins the court of Oda Nobunaga.

In both dramas the characters relive part of the day to make changes and avert danger or bad decisions.

Both about school life and the impact a teacher can have on the lives of the students

Stories have similar vibe. Both deal with school life and both female leads are out of place in their own ways (one as a student, the other as a teacher). Also as the background stories of the leads is slowly revealed, you gain an understanding into why the characters behave the way that they do.

Sequel of the Rurouni Kenshin .... A must watch before watching Rurouni Kenshin: The Legend Ends

Parent story ! you must watch it before watching Rurouni Kenshin: The Legend Ends

Both dramas have same actress, she playes similar character (her behaviour and her job too, MDS inspirated IHYV in my opinion). IHYV is mix of comedy, romance, thriller and justice drama, MDS focuses more to relationships in family, guilt, and its consequences. MDS reminds me work of Thomas Hardy, because you can't avoid your past, it will be hunted you and it can destroy you.

Set in the same work force; making CMs. Only difference is, is that the film is about CM awards and the Drama while set in the CM-verse; it's main is a love story but I recommend if you do enjoy the CM-making-world setting.

While in Bad Family you have a fake famly, in Family Outing their blood relations are real. What makes them so similar is: the comedy, the tone, the mix of screwball characters and the bonding moments.

If you liked one, you're going to enjoy the other too.