They both have Joo Won as a main lead. Both are action dramas. In both dramas Joo Won's character is kind of an underdog.

Also a tvn drama. In both dramas the leads know each other and meet after several years. Both dramas have Song Ji Hyo as the female lead.

They're both tvn dramas, and both main leads have exes who get between the main couple.

Both dramas deal with the law. Pride and Prejudice focuses on the prosecutors whereas You're All Surrounded focuses on the detectives. In both dramas the OTP has history involving a crime in the past.

Both dramas have Moon Chae Won as the female lead. In both dramas the female lead defies her family.

Both male leads went to prison when they were innocent and both seek a heiress to get their revenge.

Han Ji Hye plays the main female lead in both dramas. Both dramas deal with enterprises where the president is corrupt and very powerful.

In both the leads pretend to be a couple. Although in PM&I, they pretend to be married while in MND they pretend they're engaged.

It has most of the same comedy vibe. In one they're pretending to be a couple, in the other one, one of them pretends he is gay.

Both dramas are more than 30 eps. Both have the whole birth secret storyline and they deal with inheritance of a family company.

Same director, same feel (at least for the first episodes of DS). One has a medical-spy plot with political implications, whereas the other concentrates on the political-spy part.

Both dramas are melodramas which both a childhood and adult part. Both dramas make you cry episode after episode because everything that happens to the main characters is so sad.
Also the shipbuilding theme in May Queen is comparable to the Fish Farming theme in Golden Rainbow.
Kim Yoo Jung plays the younger version of the female lead in both dramas.