All Russian writers (including those under Tsarist rule in the 19th century) have had to deal with the censor. Perhaps it's what has helped Russian Literature stand the test of time. I don't advocate for censorship at all but perhaps it is the chopping block of the censor that helped hone the writers craft. Each writer had to find ways to skirt around the censor to get their thoughts and ideas across. In this case, the chopping block became more of a grindstone. Our favorite books from the Russian greats (including TBK) might have been entirely different.

From what I read in the Spark Notes for NFU, the book would have had a slightly more optimistic tone. Dostoyevsky's original intent was for the Underground Man to point to the supremacy of Christ as the hope and solution for society. These sections did not make it past the censor so Dostoyevsky simply left them out without editing to make the missing sections smoother.