Heh. Well, I could dodge and say that the differences are the same as between western and Russian fiction generally, but that would be no help for you. I would say that the Russian science fiction tends to pose moral questions. Not simply moral dilemmas, but how to think about unprecedented circumstances. What is important is not so much the action but which path the main character takes. This is pretty much in keeping with Russian literature generally. It shows up strongly in Fyodor Dostoyevsky (e.g., "Crime and Punishment", and "The Brothers Karamazov").

There is a wonderful novel by Mikhail Bulgakov, "The Master and Margarita", in which Satan comes to Earth and raises havoc. A side story of the divine disorder is a meeting between Christ and Pontius Pilate, in which they are reconciled. I can't describe how wistful I felt about that reconciliation.

In another novel, by Vladimir Savchenko, "Self Discovery", he recounts the history of a biological researcher who devises a way to make perfect clones. So he tries it on himself, not without peril, because the process involves him being more or less dissolved so his template can be captured. He is reconstituted along with his copy. The clones are greatly confused by this state of affairs, but he nurtures them to knowledge, producing about half a dozen or so. The household becomes more uncomfortable for everyone, due to the confusion over personality, so the clones all decide to depart and go their separate ways as individuals, which they do. The experimenter is sad to see them go, but he understands the necessity for a person to be a person, not a mimeograph copy. In time, he undertakes a final experiment, but the process fails and he is gone. Afterward, not knowing this, the clones mutually decide to have a reunion and they return...to find their template forever gone. This is a blow and they ponder together how ought they to live, now that he is gone, in honor of his memory. Sometimes, what you do next is not entirely free of attachments and obligations. You have to keep in mind in the reading, that the theme applies to the experimenter as well as his clones.

Anyway, there are others of a similar spirit. I don't know if this is a helpful answer. If you enjoy science fiction broadly, I think you will find much in Russian SF. I would be hard pressed to find American counterparts, but Ursula LeGuin's novel, "The Dispossessed", comes closest. It is the story of a moral temptation to a man who retains his integrity. Possibly also, Ray Bradbury, though I am not thoroughly acquainted with his work.