Yi San is about Dong Yi's great-grandson. The old king in Yi San is the same character as Dong Yi's young son. The main romance plot is also quite similar. Both kings in the drama have a queen who can't give him a child. The king's main love interest is a humble ordinary young woman with a special talent in arts (Dong Yi plays haegeum while Song Yeon from Yi San loves to paint). (Something funny for me is that the actresses for the female leads, Han Hyo Joo and Han Ji Min, looks similar). The main female love interest also has a warrior brother like who has a one sided love for her. You could also notice the similar directing style of both dramas, both were directed by director Lee Byung Hoon (not the same person as actor Lee Byung Hun) who also directed Jewel in the Palace. They also have the same writers (Jewel in the Palace writer is different though, writer for Jewel in the Palace is the one who wrote Queen Seon Deok).

=> Strong female lead characters that started in very low positions (though the female lead in QSD is actually a real princess that didn't know her identity)
=> Female lead pretends to be a man at the earlier part of the series
=> Two equal love interests (Bidam vs Yushin, Tahwan vs Wang Yoo), even today, fans of both series argue which of the two love interests does the female lead love more
=> A third male character (Alcheon, Taltal) is technically not a love interests but is very supportive of the female lead
=> Actors Jung Woong In and Kim Jung Hyun (different actor from the one in Mr Queen and CLOY) are in both dramas and both their characters are on the evil side in both dramas
=> Female lead often has to fight with other women of high positions in the court before she reached the top position.

1. Lee Joon Gi is male lead in both these historical dramas. We know he did a lot of historical dramas, but we can argue that these two are most successful. Iljimae gave him Top Excellence in SBS Awards as well as nominations for Baeksang while Moon Lovers gave him international popularity.
2. Lee Joon Gi is rivals with a half brother for the love of the same woman. Except in Iljimae, he and the half brother do not know they are siblings. Also, there is less focus on romance in Iljimae.
3. Lee Joon Gi wears black mask in significant parts of both dramas (though the reasons for wearing masks in both dramas are different)
4. Actor Jo Min Gi plays Lee Joon Gi's dad in both dramas.

*Interesting trivia: Kim Yoo Jung, the female lead in Moon Lovers' rival show Love in the Moonlight/Moonlight Drawn by the Clouds, actually plays the child version of the female lead in Iljimae.

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).