It's also interesting to consider each character (disregarding minor characters) all of as an orthogonal dimension of a single person (by no means scientific): the inner-monkey (Dmitri), hyper-intellect (Ivan), spiritual/altruistic (Alyosha). From this perspective, the work is a solipsistic study on how inner-conflict manifests outwardly into the world.
Karamazov was much harder for me to read than C&P or The Idiot, and I liked the other two best.
That said, it's well worth it to read the famous passages, they are incredible prose
I don't think the intention was to appeal to the west but I think it does make it easier for westerners today to approach and appreciate his work.
Maybe it's harder to appreciate it now, I can definitely understand why it would be.
Western scholars love him for some reason (as the study of the constantly ongoing brutality of Russian culture, perhaps?)