Psycho VS psycho

Best Fit

• Mouse  ( This is a cat and mouse murder game with a lot of players that has you questioning  everyone. Literally about people with the psychopath gene and they play more than just mind games. The main is cop kind of unhinged too but so were most of the characters.  )
• The Devil Judge (FL and one of the MLs(the judge) both psychos who play the law. Questions of morality pop up. Does their trauma justify their actions?)
• Flower of Evil -A who dunnit with some romance. Who is good? Who is evil? Who can fool who in the end? 
• Beyond Evil ( psycho cop, serial killers and conspiracies)

Kinda Fits 

• It's Okay to Not Be Okay -Mostly a romance about two damaged souls with a bit of conspiracy/mystery on the side. They play games with each other but mostly the FL driving the madness.
• Strangers from Hell - One lead is driven to the edge by the other.
• The Veil - ML is a super spy who kind of unraveled the more you watch. He really went above and beyond to catch his enemies even to his own detriment

Not sure but worth looking at

• Evil Minds ( did not finish watching but fits what your looking for)
• The Guest - This has a  a supernatural element (ghosts, possesion, exorcisms etc) and the leads are obsessed with finding the culprit. 
• The World of the Married - What happens when love turns to hate. A woman scorned and a desperate man. 

I'm not sure what u mean by "Psycho" because not sure if there are dramas with both sides real psychos .

psychological game between cop and killer where some point both are psychos (not so normal and decent):

Lucifer masterpiece revenge which almost drives crazy target cop

Hello Monster great drama, very smart ML vs/and kind of with psycho serial killers

Duel  

Gap Dong 

A Man's Story  SML is almost villain and quite psycho, also it's rare case when bad (but very charismatic) guy kind of wins (every character in drama, including his father and sister, except for FL are against him but he never looses, he is very smart)

Psychopath Diary this one is kind of comedy but maybe only one where both are real psychos (guy who thinks he is serial killer and real serial killer) really good watch