Thank you for posing the question, as it has helped me arrange a few thoughts about both the writers.
When you read the works of Tolstoy you get a feeling that you are listening to the words of a saint. Tolstoy's work can be compared to a mighty ocean or a pinnacle of glory beckoning us, the humanity, to shed our baser nature and realize the true purpose for which God has given us life. Stories like, Little girls wiser than men, How much land does a man need, God sees the truth but awaits,Prisoner of the Caucasus, The forged coupon, The death of Ivan Ilyich, The Raid etc make a profound impact on the reader and the effect is nearly cathartic. Thomas Mann wrote of Tolstoy's seemingly guileless artistry: "Seldom did art work so much like nature."
Dostoevsky is not as easily accessible to the reader as Tolstoy is. “Dostoevsky…the only psychologist from whom I have anything to learn." – Nietzsche (1887)
"Dostoevsky gives me more than any scientist, more than Gauss." – Albert Einstein.
Dostoevsky is not for the ordinary reader, in the sense that he is not a story teller. It can be said he is the first novelist who uses the narrative mode to inquire into the nature of thought and reality. Mikhail Bakhtin argues that “Dostoevsky's works are essentially dialogical, unfolding on the basis of interaction between autonomous voices, as opposed to monological, where plot and character unfold within the confines of a single authorial universe.”
The novels of Dostoevsky resonate at different levels. His nature of inquiry is internal and inquisitive. Any one who has read Brothers Karamazov will understand how the novel is not about the Karamazov family alone but also about the Russian society at such a time, Religion through the eyes of a believer, nonbeliever, agnostic and a cynic. Dostoevsky’s novels and short stories are an unrelenting exploration into the nature of reality seen through a complex prism of belief, social class, sin and atonement. Perhaps it can be best summarized in his own words
“The awful thing is that beauty is mysterious as well as terrible. God and the devil are fighting there and the battlefield is the heart of man.”
― Fyodor Dostoevsky,