Both Goguryeo dramas. Goguryeo is rarely featured in kdramas if ever so I'm glad there's another one after so many years. Fans who will watch River Where the Moon Rises should check out the representative Goguryeo drama, Jumong.

If you want to check out Song Joong Ki performance in another work before watching Vincenzo, please consider checking Innocent Man first instead of Descendants of the Sun. It's another modern work of his and he shows more acting skills in it than DOTS. (Actually for me, he was the best in Tree with Deep Roots and Arthdal Chronicles, but some Vincenzo fans might not like them as much due to them being serious sageuk so I suggest Innocent Man first).

I know the dramas are kinda random, but if you came to see Iljimae to see Kim Yoo Jung in her child actress days, then I definitely recommend you at least see her scenes in Grudge the Revolt of Gumiho. It's her first lead role in TV. If you see her romancing Yeo Jin Goo (her lover in Moon Embracing the Sun) in Iljimae, definitely check out Gumiho Fox Child for her romance with Lee Tae Ri (formely known as Lee Min Ho born 1993, he's another lover of Kim Yoo Jung in Moon Embracing the Sun).
In both dramas though, Kim Yoo Jung plays a good kind hearted girl. There are also a few scenes in both dramas that are quite similar. In Iljimae, Kim Yoo Jung enjoys the company of a bird while in Gumiho Fox Child Kim Yoo Jung enjoys following mostly fireflies and sometimes butterflies. Another scene is where Kim Yoo Jung is helping one of the young male characters heal their wounds. And another one is where Kim Yoo Jung's adult version Han Hyo Joo is enjoying the lanterns while being watched by one of her love interests in Iljimae is similar to Kim Yoo Jung in Gumiho Fox Child where she was also watching the lanterns while her male love interest looks at her so lovingly.

=> There is a prophecy in both dramas about "two suns cannot exist in the same sky"
=> Same child actors of the 2 main leads which are Yeo Jin Goo and Kim Yoo Jung (personally I don't ship the two former child actors unlike many but it's still interesting too see that their only scene together in Iljimae is so similar to their first meeting in Moon Embracing the Sun, falling petals also feature in some romantic scenes of them both in both dramas).
=> Two half brothers who are rivals for almost everything, half brother envies the male lead for the attention he has with his parents (or their foster parents in Iljimae), to everything the male lead has compared to the half brother, to the female lead that loves the male lead over the half brother (interestingly, the male lead in both dramas are both the younger half of the two brothers and also also the sons by the legal wife of the dad).
=> Eunchae's good heartedness (female lead in Iljimae) reminds me of Yeon Woo (female lead in Moon Embracing the Sun), this is especially true with the young Yeon Woo (Kim Yoo Jung). Han Hyo Joo and Kim Yoo Jung are so in sync with each other as actresses and are really good in playing these beautiful kind hearted noble girls that every male lead likes. (I personally feel Han Hyo Joo would have really rocked the role of Yeon Woo, Yeon Woo with her memories is especially so similar to Eun Chae).

Princess Man is the sequel to Tree With Deep Roots (not the same producers, but the kings in Princess Man are the ones that follow the kings in Tree with Deep Roots historically). There are fictional elements in both dramas, but at least the names of the kings and the ministers are all real people. Tree With Deep Roots tells some parts (although some may be fictional) of King Sejong's accomplishments and on how he created Hangul, Korea's alphabet. It started with the reign of his father, King Taejong. Princess's Man, tells the story of King's Sejong's sons King Munjong and Grand Prince Suyang and what will eventually happen to their families. Han Myung Hee (a character that features in Princess's Man) also appears as a minor character and is mentioned by name in Tree with Deep Roots.

Both dramas feature Moon Chae Won in hanbok (where she looks extra pretty). Even though her role in Painter is only minor, it's still worth watching because it's her breakthrough role and her role in it is so unique. She has chemistry in her partners in both dramas that led her to win best couples with her respective partners. Both dramas are really great in general (in fact both were nominated for Baeksang). As of February 2, 2021, these are also the only two dramas that got MCW to be nominated at Baeksang Awards.

Both dramas are set in the Joseon dynasty. Villains in both dramas are kings (or will eventually become King in Princess's Man). Both main couples in both dramas are kind of "Romeo and Juliet" since the parents of the female lead is an enemy of the male lead (though there is less focus romance in Iljimae). Park Shi Hoo features in both dramas.

=> Same female lead acted by Moon Chae Won
=> Both male leads are acted by very handsome and charismatic actors
=> Both male leads are suspected criminals
=> Both male leads have a sister they love and protect
=> Moon Chae Won and her respective male leads have great chemistry in the dramas.
=> Both dramas answer the question: "Can love overcome all hate and evil?"

Tale of the Nine Tailed fans, if you are enjoying Lee Tae Ri as Imoogi, please let me inform you that it is not the first gumiho drama that he has acted in. 10 years ago, he acted in a drama called Gumiho Tale of the Fox's Child/Grudge the Revolt of Gumiho. He's only a supporting character here but his character is also quite important since he is the love interest of the gumiho child (played by Kim Yoo Jung). Notice also that he and Kim Yoo Jung also acted in Moon Embracing the Sun as child actors (although his love for her in Moon Sun is one sided).

Moon Embracing the Sun fans, please watch The Princess Man. Both dramas came out around the same time period (late 2011-early 2012). Both are also about romance and love stories between not just one but at least 2 couples.

I know the dramas are kinda random, but I just want more people to discover more of Moon Chae Won's works. The few similarities of both stories include a love story where the male leads have great chemistry with Moon Chae Won, a couple whose love must face a lot of difficult challenges, one of the main leads lies to the other about his/her real identity which causes problems later. In addition, both dramas also show Moon Chae Won's character being a strong female lead, at one point we can see her saving the male lead (Bonus: the male leads in both dramas actually acted together in 2008 kdrama Iljimae, so watch that if you want to see both guys act together). I find it also interesting that the male leads in the drama also have good friends who are both very persistent in loving their own respective love interests who are reluctant in accepting them at first
For Flower of Evil Fans -> you can see in Princess Man Moon Chae Won's top notch acting, Princess Man should be the first of her other dramas you watch since she won or is nominated for more awards for this show than any of her dramas as leads (including 2012's Innocent Man).
For Princess Man Fans -> as you've seen Moon Chae Won's great acting already, you can see in Flower of Evil her most recent work (2020). It's the drama that is worthy of her acting skills and her first and most acclaimed drama after 2013.
Trivia: Producer Yoo Sang Won is a producer involved in both dramas. He also did Lee Joon Gi's 2014 drama Gunman in Joseon

They have the same writers. They main character is also a twin in both dramas. There is a prophecy about the twin characters in the drama that is important to the plot. They also both have complex characters, meaning likeable villains, protagonists with a dark side, and characters which we won't understand at first if they're good or evil