Light, sweet, fluffy and humorous. Both take some cliched tropes and turn them into something refreshing. Devoted MLs, irritating SMLs.
From the same writers (Hong sisters), both shows are high fantasy + romance. They have strong female leads with supernatural abilities who is on a mission related to her past and can fight well. Both have good special effects and some comedic elements to it as well.
Both are historical romcoms with a focus on women's issues. Both FLs want to be free of marriage. Rookie Historian takes place in the palace and has more politics, while SRI&J is set within villages and is more comic. Both are fluffy and feel good.
Both are light feel good comedic romances set in historical period. 100DMP is heavier on court politics while SRI&J is sillier.
Both shows are slow, peaceful and focus on living in the moment. They are set in similar environments amid nature.