=> Both are high profile sageuk projects starring Yoo Ah In
=> Both were shown in 2015 (Six Flying Dragons ended in 2016)
=> Yoo Ah in won many awards for his portrayal in both sageuk projects
=> Yoo Ah In's role has a similarity in both dramas, he's someone who doesn't obey his father's wishes.
=> Because of the success of these two projects (along with Yoo Ah In's 2015 movie Veteran), 2015 was called "A-in-shi-dae" (Ah In era).

I recommend Dong Yi for The Throne fans since it gives character to the mother of King Yeongjo, the woman who was only mentioned as a lowly concubine in The Throne. Dong Yi is the love story of Yeong Jo's parents as well as the political happenings during Yeongjo's father King Sukjong's era. Dong Yi also shows the rivalry between concubines including Dong Yi (Yeong Jo's mother) and Jang Ok Jung (mother of Yeong Jo's brother, who was the king before him as mentioned in the drama). Through watching Dong Yi, the audience will understand why some people in The Throne think King Yeong Jo killed his brother for the throne as well as how Dowager Queen Inwon was Queen Dowager despite her not being King Yeong Jo's mom.
For Dong Yi fans, The Throne movie shows one tragic aspect in the long reign of Dong Yi's son Yeoning aka Yeong Jo: the events that lead Yeong Jo to put his son Sado in a box which led to his son's death.

In both Jang Ok Jung and The Throne, we see Yoo Ah In playing a Joseon Royal. King Sukjong (Yoo Ah In's character in Jang Ok Jung) is also one of the main characters in Jang Ok Jung. This means that Jang Ok Jung is a show that might be enjoyed by The Throne fans since it has both Yoo Ah In plus the audience get to know more about King Sukjong (who is only barely mentioned in The Throne). One must keep in mind that Jang Ok Jung has a little twist in that it tends to be more sympathethis towards Sukjong's concubine Jang Ok Jung, who is more historically known as the more villainous concubine. Jang Ok Jung is the mother of the brother of Prince Sado's father, King Yeongjo.

As The Red Sleeve doesn't show much of how a King's grandson was the Crown prince instead of his father, a fan of The Red Sleeve can watch The Throne to understand more of the situation.
For the Throne fans, they can watch Red Sleeve if they want to know the story of Sado's son. Red Sleeve is the show they should watch if they want more focus on Sado's son's romance. There is also some politics in Red Sleeve, but the love story has a bit more focus (especially the last 2 episodes).
In contrast, the 2007 drama Yisan tends to have more focus on the accomplishments of Yi San as Crown Prince then King (though romance is also important in this show).

Yi San is a 2007 drama about Sado's son. It covers about the same time period as the more recent Red Sleeve 2021 drama except that it has greater focus on politics. If you want to watch a drama which shows more focus on Sado's son's politics as a prince then as a king, Yi San 2007 drama is the show for you. Yi San 2007 also shows more on how Sado's son was acting as his father was dying in the beginning episodes.
For Yi San fans, you can watch in The Throne another portrayal of how Yi San's father died.

=> Cinderella like story (a girl who is either poor or lost everything has a love story with a rich guy)
=> Han Hyo Joo is the female lead in both
=> Bae Soo Bin plays the good hearted oppa/orabuni who has one sided feelings for the female lead
=> female lead becomes a friend of a family member of the male lead (grandma of male lead in Shining Inheritance vs the official wife of King/male lead in Dong Yi)
=> a woman (Jang Ok Jung in Dong Yi vs Yoo Seung Mi in Shining Inheritance) who has known the male lead for much longer than female lead does evil/bad things especially when she noticed male lead loves the female lead more than her.

=> Both are good dramas for lovers of political angle in historical dramas
=> Jang Hyuk is in both dramas, the relationship between him and the kings in both dramas and how he considers them are very important and very instrumental in both dramas

Both historical dramas star Kim Yoo Jung as the female lead. In both she possessed a special talent that helps the male lead (dancing vs painting). There's also a second male lead who fell in love with both her characters very fast.

=> Both dramas depict various murder cases throughout the episodes
=> the main characters are profilers who try to identify the suspects by analyzing their behavior
=> For me: Through the Darkness>Criminal Minds, although the actors playing the criminal suspects in criminal minds are really good
=> Don't expect any romance between the male and female leads for both dramas

Dramas have similar premise. A person with a special syndrome who has very high IQ enters into the professional world. The special doctor/lawyer also seems to have more compassion/humanity for people than those around him/her who care more for worldly honor than an individual's dignity/personal choices (the last sentence is quite hard to explain but the people who watched both shows will understand what I mean).
There are other similarities aside from the basic plot/story. Both shows got a lot of praises while airing, raising the profile of their respective actors who played the autistic character more. Good Doctor received a lot of awards and there's a large probability Extraordinary Attorney Woo might receive many awards too. The US also decided to have a remake of both shows.

Same story. Philippine version is based on Korean version of the drama. Lee Joon Gi and Moon Chae Won are topnotch actors. those who will watch the Philippine version must definitely watch the Korean one because of their actors.

Both are about a newly found dynasty. There is this king (the founder of the dynasty) with many sons. The main character in both dramas is the son of the king who is not the crown prince but is talented yet ruthless enough to become king. Both are morally grey characters. Both loved a woman but married someone else because the woman they loved is ineligible to become empress. Some of the brothers of the main character were also killed by the main character before they became king.
In addition both are SBS dramas that aired within a few months of each other. Both also have lots of martial (though in Six Flying Dragons, the male lead does martial arts but the best martial arts belong to the other characters as opposed to Moon Lovers where the male lead has the best martial arts skills).