A historical drama featuring a star-crossed love triangle starring Ha Ji Won. The stories may be quite different but if you watched Empress Ki or Damo, and liked either of them really well, you must obviously have become a Ha Ji Won fan because since she's the lead of both shows. Therefore, I am recommending Damo to Empress Ki fans and Empress Ki to Damo fans. Both dramas feature Ha Ji Won as an orphan poor girl who has to overcome a lot of trials in her life. Both dramas are also her sageuks where she shows a lot of swordfighting and other action skills. Also in both shows, it appears that she had always loved a man who is kind and caring, but somehow became drawn to another man who she was not supposed to love. The love triangle in both dramas have great effects on Ha Ji Won's character since they both have/gave her something very important to her.
I suggests fans of either dramas watch the other since Ha Ji Won is fantastic in it. Also, because Damo was such a great drama for its time in 2003 but is somehow currently ignored because of so many newer dramas.

Need more shows where Kim Yoo Jung shows her versatility as a child actress? Grudge the Revolt of Gumiho is for you
There are a lot of elements similar to the stories:
-> Both are sageuk, but both dramas contain fantastical elements (shamans, curses, prophecies)
-> the sweet and talented beautiful young girl believably played by Kim Yoo Jung
-> basically, both Kim Yoo Jung characters entered a place (palace in Moon Embracing the Sun, Yoon’s house and surrounding town in Grudge the Revolt of Gumiho) and her charm and beauty impresses some powerful adults (king in moon sun, head of Yoon household in gumiho) making rival girls jealous
-> there is a sweet childhood love story in both dramas, except in Gumiho, the childhood love story is not the main plot.
-> The guy playing Kim Yoo Jung’s lover in Gumiho is Lee Tae Ri/Lee Min Ho 93 (aka the young version of Yang Myung in Moon Sun)
-> The above basically means that if Yeo Jin Goo (young Hwon) and Kim So Hyun (young Queen Bokyung) have Missing You, then Yoo Jung (young Yeon Woo) and Lee Tae Ri (young Yang Myung) have this drama Gumiho fox child
-> Find the scene where Kim Yoo Jung/Han Ga In are following butterflies?—> there are at least two cute scenes in Gumiho where Kim Yoo Jung and her lover are enjoying fireflies. Both dramas actually have two young couples meet because Kim Yoo Jung’s characters were following insects
-> The main villain family in both dramas both have the last name Yoon. Both fathers wanted to kill Kim Yoo Jung’s characters for their benefit and both daughters are evil, ruthless, and are jealous of Kim Yoo Jung’s characters (especially because the guys they like like Kim Yoo Jung’s characters)
-> SOME SPOILERS: Kim Yoo Jung’s characters both “died” in these dramas, and her lovers in the respective dramas were too helpless to save her. Both dramas also make people feel for the grief of a family/lover, for the death of an innocent young girl.
-> SOME SPOILERS: In both dramas, after the “death” of Kim Yoo Jung’s characters, both characters appear on the lives of other people they had affected when they were young, appearing either as a dream to the people she loved or somehow haunting those that hate her (particularly the evil Yoon girls)
-> Shamans have great involvement to the events in both stories
-> Other actors that appear in both dramas aside from Kim Yoo Jung and Lee Tae Ri/Lee Min Ho 93 are Yoon He Seok (Sungkyunkwan student who became a guard or warrior in Moon Sun/ Kim Yoo Jung’s lover’s dad in Gumiho) and Jung Eun Pyo (Eunuch in Moon Sun, Kim Yoo Jung’s biological dad in Gumiho)
Gumiho does not focus on romance unlike Moon Sun, but it has many elements similar to Moon Sun and has some romances between its complicated characters. This Gumiho show was in 2010, and I firmly believe that it was her experience in this show that helped Kim Yoo Jung prepare for her role in Moon Embracing the Sun