In both we have the typical cold dude that treats the FL as trash and she is dumb as trash too. But he still develops feelings towards the FL.
Also, Itazura Na kiss at some point involves a doctor-nurse relationship.

This drama just started but we can see that (even from the synopsis) this is a romance between a south korean and a north korean. King2Hearts is also telling us the story about a north korean soldier (which is the woman) and a south korean prince.

Very different plot but better story. Way more complicated in all kinds of ways, longer, sadder, worst?
Same actor: Lee Joon gi~ but acting all the other way different. Em, dark prince? Probably suits him more.