Scrapped Princess, Akatsuki no Yona Recommendations
The plots do differ but they do share elements, a spoiled Princess surviving in the wild with only a few caring guardians and is the target of everyone, fantasy elements, great animation and music.
Both have a deposed princess on the run for her life protected by a small band of followers. Fantasy elements feature in both, as do intriguing characters and story.
Both are about a princess fleeing the kingdom. Both Yona and Pacifica are wanted by the kingdom and both girls are in need of protection and get that protection by someone close to them.
Lastly, both Yona and Pacifica are super duper kawaii
Both princesses chased out from their home and they are on the run
I know a few others have recommended the two but the main thing I would like to add is that the princesses in the two stories are VERY similar characters. If you thought the interactions between Pacifica and her adopted brother were cute and funny, you'll LOVE the dynamic betwen Hak and Yona. Yona has a little bit more of the feel of a comedy, its lends itself often to really cute digressions, but maintains the serious plot of a runnaway princess who transforms from "useless" diva into a strong leader