Both dramas have quite a dark feeling to them compared to other dramas, and have two main characters going down a dark path with people chasing after them. If you liked one, you'll like the other.
In both dramas, people from all over the country are taken somewhere and forced to play extremely high stakes games where death is likely. They're both extremely violent, and don't shy away from showing anything you normally wouldn't see from dramas. If you liked one you will without a doubt like the other.
Both dramas are set in the same universe as each other, dark hole taking place soon after the events of save me. They are mostly unrelated, however Dark hole has a cameo from the father from save me and also has a cultist storyline.
Both dramas feature characters trying to survive an apocalypse, where people are being infected with a curse that tempts them with their pasts to become violent and kill other people.
Both have similar situations, characters suddenly being forced into fighting beings beyond their comprehension. They have the same main actor, and a similar feel to them.
They are both about a cult manipulating the people involved in the main character's life. Both are unnerving and unpredictable which keeps you engaged throughout.
Both dramas are about a normal world suddenly being swept with a virus that turns humans into monsters. Packed with suspense and horror, if you liked one you'd like the other.
In both dramas characters end up at a deserted place and must struggle to stay alive against various trials. Both seemingly have someone controlling what happens.
Both dramas are about a virus suddenly being released and turning humans into monsters and the alive humans trying to fight back. In Kingdom the virus turns them into Zombies, and in Search the virus turns them into monsters with great strength that can infect humans they attack or kill.