Tempest (2011)

Both are historical dramas where main lead actress disguises herself as a man. SKKS concentrates on romance while Tempest concentrates on solving some sort of crimes.

Both are historical dramas. In both dramas they tells you a story in a comedic yet teaching way about two very different yet similar islands of Japan and South Korea.

In both dramas the female lead is somewhat similar in the aspects that she wants to do something with her life instead of just being stuck at her home city.

Both are historical dramas, albeit from different eras. The reasons are different, but the female main characters both live disguised as men. The Tempest is a sort of fantasy story loosely based on real events while Onna Nobunaga is an alternate take on history and a re-writing of a real person. There's romance in both, but The Tempest is more character-driven. Onna Nobunaga is a bit more realistic in some aspects and there are lots of fighting scenes. Onna Nobunaga is shorter because it's a two episodes special.

both present the situation of an extremely capable woman in times women had little to no perspectives on getting an education and using it for the common good. They aren't greedy for power, but want it to save the state or improve the quality of ordinary people's lives. Their idealism comes in pair with an acute political sense. Even though they're surrounded by the men who love and admire them, their advice is often disregarded, their possibilities limited and their lovers would gladly just put them in a cage so they wouldn't get hurt. You got your fun, girl, now go home and let the boys play.
Both are gender-benders (short arc in Empress Ki, more in Tempest) and hide their identity. Both have multiple love interests. Both become a ruler's concubine. Empress Ki has stronger rivalry in the harem, while in Tempest even though the harem is a scene of a financial schemes, women are in comradery.