Both deal with voice calls and helping victims that are affected.
Both shows have the same title 'Voice'.

Both MCs have abnormal abilities. In voice the MC has heightened hearing therefore making her hear sounds and voices that no one else can hear. While in Children of a lesser god, the MC is able to relive the moments of victims deaths just by touching them or using a photo of them. Both MCs use their powers to their advantage to solve cases as they both work in a police enviroment. In both shows there is a serial killer. Both have partners that are not romantically interested in eachother. Though in children of a lesser god there may be some questionable scenes thrown around - that's up to your interpretation.

Both shows have MCs that have superhuman powers. In memorist, the MC is able to look through people's memories just by touching them while in Voice the MC has heightened hearing, thus hearing things. voices and sounds that no one else can hear. Both MCs use their powers to their advantage when tackling cases. Both shows are set in a police enviroment.

Both MCs have a psychic ability. In both shows, the MCs are able to look through memories of other people through touching them. Both MCs work in a police base setting and use their powers in order to get closer to the case. While in Memorist, everyone accepts the fact the MC is a psychic but in Children of a lesser god, it is not the case. The MC struggles to convince people that her powers are legitimate and it becomes one of her struggles throughout the show. Another difference is that in memorist the MC can look through all memories but in Children of a lesser god the MC can only look through the moments before of the victims death.

Both shows have the questioning topic of "who is the real killer?"
Both shows have the Female lead starting off as trusting but slowly looses trust and becomes indecisive.
Both shows have the talk of Psychopathy but Voice 3 takes it into a darker point of view while Psychopath diary has a little comedy in it, which doesn't change the fact that the show is dark at sometimes too.
Psychopath diary can give you the same thrill as Voice for sure. In fact nearly every episode has a cliffhanger.
I recommended Voice 3 because it's the most darkest but to fully understand the story you need to watch Voice 2 as it is the baseline of the plot itself. A continuation basically.

Both shows follow the forgotten childhood friends trope.
Both in which the Main Lead have memory loss from their childhood due to traumatic experiences. The forgotten childhood friends are disguised within the story and slowly make its way to the surface.
Children of a lesser God focuses more on the childhood friends aftermath, which is something Quiz of God didn't do.
Children of a lesser God is about detectives investigating a hidden underlying Cult while Quiz of God is about a team of Autopsy Doctors working with the Police to find out who is the hidden mastermind.
Both in which the Villains personally know the Main Lead so you can emphathize their actions.