Dostoevsky employs two different strategies to represent individual psychology. In Part One, he uses "stream of consciousness," in which the narrator theoretically express whatever comes into him mind without censor. In Part Two, he has the narrator engage others in behavior that is both self-destructive and destructive to others but leaves the narrator's motivations open to interpretation, which compels the reader to try to enter the narrator's mind. Which of these two techniques better expresses psychological realism?

Great question! Ultimately, the answer to your query is rooted in opinion but here are some thoughts that might help guide you answer this prompt.
Psychological realism is a literary style that aims to replicate the inner thoughts and hidden motives of a character as precisely as possible. Authors who employ psychological realism, such as Fyodor Dostoevsky, are frequently more concerned with inward characterization than they are with the plot. The result is often a gritty examination of human nature that is unflinching in its portrayal of the ugliness that can grow in the human soul.
Dostoevsky’s novel Notes From The Underground is written in the first person by a bitter former Saint Petersburg civil servant. The unnamed narrator is caustic and unreliable in his narration; Dostoevsky clearly expects the reader to question the sanity of the narration! The novel explores this ailing man’s mental state and his twisted, incomprehensible motives for his actions.
Part I, or “Underground”, is relayed in a stream of consciousness and is much more philosophical than Part II. The narrator expounds his varied philosophies, rants about events from his past, complains of his social status and acknowledges that many readers will find his ramblings bewildering. In Part I, the reader is introduced to the narrator and exposed to his contradictory value systems.
Part II, or “Apropos the Wet Snow,” is a narrative that displays how the narrator lived out his bitter philosophy with former friends and lovers. Most readers are repulsed by the narrator’s treatment of others, particularly his savaging of Liza.
I feel that Part I is the best example of psychological realism in Dostoevsky’s novel. This is because Part I mirrors the thought processes of the deranged protagonist and offers the audience a clear, accurate window into the mental depravity of the narrator.