Both are mature dramas where most of the characters are complex showing you that humans are done of qualities, but also imperfections. A strong female leader, lots of suspicious motives behind the attitudes of each character. But every one of them are commited in this process of getting better human beings.

If you are looking for a drama with more mature characters, where no one is 100% good or 100% evil, both dramas share that.

You'll find very appealing characters and a storyline that has romance, drama, revenge, politics and strong female characters (Go Hye Ran in Misty and Choi Yoo Jin in K2).

In both dramas you have a mysterious murder that impacts all the story.

Both dramas are about a person being replaced by other of the same appearance but with a really different personality.

Both dramas have strong leader females.
Both dramas portraits the characters in an mature and adult way, instead of the childish and clingy behaviour of other dramas.
Both dramas are remakes of notorious western series (US and UK)..

Both dramas have strong leader females.
Both dramas portraits the characters in an mature and adult way, instead of the childish and clingy behaviour of other dramas.
Both dramas have a mysterious murder that will impact all the story.

Both are mature dramas, handling the relationships, emotions and conflicts in a very credible way.
You will have a very intelligent main female leader dealing with several defying challenges to the ethic and the normal way of seeing things.
In both series there are not the typical black and white characters. Here everyone is grey, meaning that every person has their virtudes and weaknesses.

Both dramas portraits the relationship between characters in a more mature way. The dialogues are clever and deep.

With each of this dramas you receive more than a cliché romance.