Done around the same time period, 2006-2007, both shows are different retellings of Hwang Jin Yi. If you want to focus more on Hwang Jin Yi's talent as a gisaeng, as well as colorful costumes, then you might want to watch the T.V. series. If you want to watch a depiction much closer to her real life (according to some people), you can watch the movie. It's good if you watch both though, as both shows depict two different views of the modern world on the historical Hwang Ji Ni and the impact of her charms and talents to the modern world.

Similarities:
=> Both are stories of a romance between a woman who is supposed to be a crown princess and a man destined to be king
=> A 12 year old Kim So Hyun gives a very excellent performance as the young version of the woman who usurps the crown princess position. (In a way she's actually the one who played the usurpers, not the adult actresses, because the takeover of the crown princess position from the real crown princess is done by her character in her teen years).
=> We see the male lead (or rather the young version of the male lead in Moon Sun) attracted to a girl with a butterfly in the first episode.
=> The male lead (him or his doppelganger in Rooftop Prince) has a close relative who can be a threat for high position he has (the king position in Moon Sun, being the heir of the company in Rooftop Prince)
=> Lee Tae Ri/Lee Min Ho actor born 1993 gave excellent performances in both dramas. Both his characters in a drama is a very smart young man who helps one of the main characters.

If you enjoy watching Han Ji Min falling in love with a crown prince in Rooftop Prince, Yi San is also another story where we can see her fall in love with a crown prince.
There is a great genuine chemistry between the crown prince and Han Ji Min's character despite the fact that her romance with the crown prince seems impossible.
Be mindful that Rooftop Prince fans might not like the politics of Yisan or Yisan fans might not like the modern era in Rooftop prince, but both dramas are worth watching to see a blossoming romance between a crown prince and Han Ji Min's character

Similarities
=> Both are stories of women who are considered "action" girls. They both eventually became the empress of a Chinese empire.
=> The emperor doesn't realize the girl's real identity as a woman until much later episodes. Its because he thought she was a man when he first met her
=> There's a lot of palace intrigue. The prospective bride of the emperor, basically tortures the female lead because she was jealous of her.
=> Both emperor's have a "loyal" eunuch.

Jumong might be too long for Sungkyunkwan fans, but I think its worth for new fans of Sageuk from those who watched Sungkyunkwan to try watching a historical drama that was considered one of the best in the previous decade (2000s).
Here are the similarities:
=> Jumong is one of the few dramas BEFORE Sungkyunkwan Scandal was aired that shows a "romance" between two male characters
=> The same gender relationship in Jumong is more two-sided than the one in Sungkyunkwan
=> Like Sungkyunkwan, one of the two males who might be involved in a heartwarming relationship with another man is a hairy man while the other one is a flamboyant pretty man who likes wearing bright colored clothing (the flamboyant man in Jumong being more womanly than the one in Sungkyunkwan).
=> If you are in Sungkyunkwan for strong, determined, female characters, Jumong has them too.
=> Both dramas have some episodes dedicated to martial arts competitions. Examples including archery and swordsmanship (using sword sticks)
=> Both feature an evil male character close to the age of the male leads.

=> Both are set in the Silla Dynasty
=> If you became a fan of King Jinheung from Hwarang, you can be satisfied of how he has become a great King at the beginning of Queen Seon Deok.
=> As both are only two of the very few dramas about Silla dynasty, both dramas are among the very few that can help people understand the bone rank system in Silla.
=> Both dramas have a woman who is technically not a queen, but acts and really wants to be one.
=> Both dramas offer either a beginning or an ending for the character King Jinheung. For Hwarang fans, Queen Seon Deok shows how he became a great King. For Queen Seon Deok fans, Hwanrang is a possible beginning of Queen Seon Deok's grandfather Jinheung.
=> Hwarang (youth warriors) are given importance in one drama. If you want to see a different kind of Hwarang you just watched in one drama, then watch the other one.
=> For Hwarang fans, Queen Seon Deok is what happens if the King of Silla fails to produce a Seonggol (sacred bone) male heir that continues to live a long life.
=> For Queen Seon Deok fans, I believe that the main villain in Hwarang Park Young Shil is Mishil's grandfather (see her ancestors on wikipedia to prove), so its a treat to see her family's roots on villainy.

Similarities:
==> featuring Song Il Gook who shows great range for acting characters from a distant historical era
==> the male lead undergoes training in fighting and martial arts, which are of great help to him in the future as a great leader
==> Yeo Ho Min's characters are very loyal followers to Song Il Gook's characters in both dramas
==> SPOILERS: there is a woman deeply loved by the male lead but he somehow had to end up with another woman (whom he doesn't love as much as the other but she was a good wife for him and is someone he learned to care a lot)

Aside from Song Il Gook and Yeo Ho Min, other actors found in both dramas include Bae Soo Bin and Lee Jae Yong (their characters in one drama are very different from the characters in the other drama)

If you enjoy Moon Chae Won's acting, her chemistry with her romantic partners, and a father and daughter chemistry with Kim Young Chul, then I am recommending The Princess Man for Innocent Man fans and vice versa.
Similarities;
==> Moon Chae Won and Kim Young Chul as a family unit. A bonus is that actress Kim Seo Ra (who was Moon Chae Won's mother in Princess Man) also have a cameo in Innocent Man as her mother too.
==> The main lead's romance with the female lead is a forbidden romance, something that may not be good for the female lead especially in the eyes of her father
==> Female lead defies her father because of her love for the male lead
==> Something happened in the main lead's life that caused him to be convicted and become more miserable
==> The male lead has a compelling reason to really hate the female lead's father

Very, very different. But I know that most Song Joong Ki fans became fans through this drama and might see him as a mediocre actor if he fails to succeed after DOTS, thus I am recommending a drama he did before DOTS which shows his capability as an actor.
The drama I'm showing is "Tree with Deep Roots". It is one of the first dramas where Song Joong Ki shows great acting. He appears on Episodes 1-4 + episode 8 or 9 (can't remember which of episode 8 or 9 he appeared). You can see how versatile his acting is.
I am not downplaying the other actors either. Han Suk Kyu is also someone who gave a really great performance as the adult version of the King Sejong played by Song Joong Ki. Jang Hyuk and Shin Se Kyung also gave great performances. The plot, while being only a fictional version of how Hangul is made, is a very plausible possibility on how Hangul is actually made. The characters are compelling.
The very few similarities they have is that, the many of the main characters, whether the possibility of being together with their loves is high or not, have rarely backed down on their principles and are always focusing on serving the people that they serve (except perhaps Jang Hyuk's character in the first few episodes of Tree with Deep Roots)

If you watch one of these two shows, the other might be interesting to see how different Han Suk Kyu plays the same King Sejong on different stories with different directors.

Both are historical dramas aired around 2007 about two of the greatest Goguryeo kings. One being its legendary founder Jumong while the Damdeok in the Legend is historically more well known as "Gwanggaeto the Great". While Jumong have less fantastical elements than The Legend, the story Jumong itself is sparsely based on a legend that the first King Jumongs has mythical origins. The Legend meanwhile, shows Goguryeo and its character as somewhat a reincarnation/repeat of the mythical Jooshin characters. There are also two women that were very different from each but both love the main guy.

I know that both stories are quite different, but I am recommending Tree with Deep Roots for Arthdal fans and vice versa because they have the same writers.
>Both dramas have:
== more twist and turns and character revelations (whether it is an additional character or something about a character is revealed
== Song Joong Ki's high class acting --> though he's only in the first 4 episodes + episode 9 in Tree with Deep Roots, it is worth watching if you want to see his good acting skills. Even if you started both shows for him, you will find yourselves also immersed on other characters as well the actors that portray them (whether it is an older version of Joong Ki's character, a mysterious swordsman, a mysterious guy with a mask, or even the villains)
== I think it's noteworthy that the shows also put importance in education and literacy. Like how the wahans or the poor Joseon people were taken advantaged because they were seen as less "educated"