The Great Doctor

Both female leads are doctors with similar personality types. They both get transported to another realm/time period. While Faith is more of a medical drama and sageuk, W is more of a modern day romantic comedy.

If you take away the supernatural time-traveling theme with the main girl, it revolves around King Gongmin, Princess Nagook and General Choi Young who seem to play a bit role in the background of the Six Flying Dragons. It's definitely a good drama to watch either before or at the same time as Six Flying Dragons to get a good background picture as to why Goryeo is looking the way it does in Six Flying Dragons.

Both dramas have fake looking special effects, time travel, and characters which look like they are doing a cosplay play. Although, Faith's are slightly better than the Holy Pearl's.

My Country is heavy on the action and bromance and less on the politics, which I think Faith can be comparable to that plus their approach to this genre is so unique. The number of episodes in Faith may be a bit draggy, but overall it's really a solid drama.

-Female Leads are doctors
-Great Chemistry between lead couple
-Beautiful Love Story
-Perfect Pairing
-Male Leads are very strong and can fight very well.

Even though Faith isn't Japanese movie, it's Korean drama, they have similar plot, they are both historical and action movies.

In both dramas main lead travel back in time( the duration of time travel differs) and now they must survive in a different time line which is unfamiliar and has different rules

Modern day FL travels to the past and falls in love with a general.
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The female lead time-travels to the past and falls in love with the male lead.

both have time travel genre, there's also a diary involve that owned by main lead actress of this two drama, the difference the way they time travel is that in Faith a doctor is being forced by someone to time travel while in Thousand Years of Love a princess who wants to die, time travel instead. they also have bitter sweet ending

Both are time slip dramas with a modern day FL and historical ML in a court setting.
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Even if the plots and the main characters are different, some characters appear in both dramas (in Faith they're young, while in The Great Seer they're older).
In both dramas there are supernatural powers (used to fight and to time-travel in the first, used for divination/geomancy in the second).

Similarities :
The story is based on Time Travel.....
They have Power struggle between royals...
Main lead travel from modern day to historical era.....
Both have parallel world

Time Travel
Destined Love
Romantic Moments
Conflicts in the Palace
Martial Arts meets CGI
Interfering with History
Modern World vs. Ancient Dynasty

In both the male lead is physically very fit and a good fighter and with his skills he rescues the female lead from danger. He watches over her and she feels protected because he is there for her. The antagonists in both are scheming politicians, so the male and female leads are helping the good side win.