Both are thrillers set in 1930s Korea that include LGBTQ main characters and a lot of the plot happening in an isolated location. imho 'Phantom' is more of an action thriller, while 'The Handmaiden' is more of a psychological thriller.
Both series are police procedurals featuring two leads with contrasting personalities and wonderful (and imho subtexty) chemistry.
Both are Republican Eras dramas (Couple of Mirrors' is set in the 1930s and 'The Message' is set in 1941) that feature two female leads with excellent chemistry.
These are my two favorite adaptations of the novel! 'The Message' is a thriller full of unreliable narrators while 'Phantom' is much more of an action movie, but both have excellent chemistry between their female leads and a satisfying story.