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).

=> both shows are written by the same writers. (people have to take note that Tree with Deep Roots was partly based on a novel but Six Flying Dragons is written by the drama writers only, but remember both dramas are based on history too).
=> Six Flying Dragons is the prequel to Tree with Deep Roots. For Tree with Deep Roots fans: you can find in Six Flying Dragons the beginnings of Joseon Dynasty, how Lee Bang Won became a ruthless King and the background of characters like Muhyul and Lee Bang Ji. For Six Flying Dragons fans,Tree with Deep Roots is about how Lee Bang Won's son became a great king, also a continuation of the fate of characters like Muhyul, Lee Bang Ji and even the nephew of Jeong Do Jeon.

=> a woman uses her brother's identity and pretends to be him to enter an all male group/institution.
=> the main group consists of 3 guys and 1 girl pretending to be a man
=> the main guy and the second guy are both in love with the main girl
=> the third guy is very cute and has a cute crush on the main girl
=> the second guy is the first to know of the main girl's identity

Now that season 2 is confirmed with new actors, I'm sure fans of the replacements will watch season 2 for them. it is absolutely necessary you watch season 1 because it is quite a complicated world and the worldbuilding is in season 1. I also hope for some appreciation for the efforts of the season 1 cast (I'm saying this seeing how most people underestimated Arthdal drama when it was airing).
Now, if you notice the drama, it is presented in many titles. If you wonder why is that, the season 1 of the drama is divided into three parts. But all three parts comprised of season 1. This particular part here is part 3.
I also recommend season 2 for season 1 fans. Please watch the drama even with the cast change.