This novel, along with 'Crime and punishement' deal with completely opposite personalities. One has a very optimistic view of the world, the other, Raskolnikov from Crime and Punishment, despises it and justifies violent crime with this mentality. Wonderful works, both of them. Unlike many, I read TBK first and decided to read Dostoevsky's other works and fell in love. Notes from the underground will always hold a sp…
Crime and Punishment, to me, seemed pretty straightforward, where we knew the problems Raskolnikov was having, and pretty sure of the ending where he'd confess and be punished (clearly from the title). Whereas The Brothers Karamazov if I remember, was somewhat more of a non straightforward plot. Where the characters were slightly less straightforward. I checked on wiki and said that Crime and Punishment was fourteen years before Karamazov, 1866 to 1880.
Besides Dostoevsky, I really liked a few of the Checkov short stories, and then Master and Margarita, which was written in the somewhat early 1900s. Not sure if those related to the existentialism you're talking about, but all unique.
I think my main like of both of these, and books in general, is the ability to see how similar humans are from centuries ago, and in different cultures. With the feeling of desire to be punished, or in a Checkov story, falling out of love with a woman and not really knowing how to end things. Being able to see relationships and similar thoughts from completely different people is very comforting. Otherwise we all could be stuck in our heads thinking about how everyone is different from you, where we're all more alike than we think.