Before I get to the main topic, a quick update on the Death Note/C&P relationship: I was indeed right, Raskolnikov's pride did indeed land his sorry person in the Gulag xD It's cold up there in Siberia...
The main similarity is indeed the philosophy of the two protagonists. Later on in the book, Raskolnikov formally discusses his philosophy with Razumihin by means of a paper; two months before the murders, Raskolnikov had written a treatise about his philosophy, which was published. In this treatise, he stated that there are ordinary classes of men, which morals tame and keep in submission/order, and there are extraordinary classes of men, (Napoleon is his chief example - Khan would be another good one) and morals only inhibit extraordinary men. Both Khan and Napoleon, even Charlemagne, could be considered mass murderers- but this is not how they are remembered. They are remembered as great men, because, as Raskolnikov puts it, they did not let morals "inhibit" their designs.
The key difference is that Light fits into the category of "extraordinary" men, as Raskolnikov puts it, and Raskolnikov himself does not. Light can execute without clouded judgement, remorse, or feeling, but Raskolnikov cannot and he realizes this eventually. He realizes he is not an extraordinary man and it depresses him quite a lot.
The other key difference is that Light never confesses, but fights till the very end and dies a tragic, rather lonely, early death. Raskolnikov eventually sees the error of his ways after confessing (he confesses because he knows he will be caught) and decides to change.
Whether their common philosophy was right or wrong is really a matter of perspective. I know that fans of Death Note intensely debate whether Light was right or wrong. Either way, people who choose to live Light's life style and follow his philosophy, right or not, will live a difficult life without love, and this was made obvious in the end. Raskolnikov instead found love in Sonia and in religion and decided to make a change in his life at the end, since he was not in the class of "extraordinary," men.
Okay enough of that.
Today I will be focusing on characterization. Now, I know that sounds boring, but think about it for a minute: why do we love stories? Why are we so addicted to television and movies? Half of the time, we love stories for their characters. We watch Ellen Degeneres for Ellen and we watch the Daily Show for Jon Stewert. We love Harry Potter for Harry, Ron, Hermione and even Neville. We love our stories because of their characters, more often than not, and we don't like stories with flat/cardboard characters.
Twilight is almost universally hated because its characterization is so poor, and the characters have no personality. The few who like the series like are tween girls who see the story as a way of living personal fantasy (who doesn't like to pretend they're a bland characterless girl who has every hot man/supernatural creature in existence after you? Even when you do nothing to merit such attraction? 😒)
So characterization is everything. One of the most appealing things about Crime and Punishment are the characters: Dostoevsky weaves beautiful, complex characters who serve as foils to each other and provide interesting contrast as well as dialogue.
Here are some basic character relationships which I found to be engaging:
Dunia vs Raskolnikov
These two are siblings, and here, Dostoevsky does an amazing thing and breaks traditional gender roles. Raskolnikov is portrayed as indecisive, is prone to bursts of ill health and fainting, irrational, short tempered, and is often a burden to his family.
Dunia, on the other hand, despite being a female, is portrayed as level headed, selfless, rational, and most of all, she has self respect. She is portrayed as a strong, intelligent woman, which is very unusual for literature of the period.
Dunia loves her family enough to marry Pyotr Petrovich, who annoys her, so that he can financially support them. But when Pyotr proves himself to be a user, and a disrespectful man who only wants her subservience, she has enough respect for herself to turn down the marriage, and uses her quick thinking to find another way to save the family's finances.
Razumihin vs Raskolnikov
The classic foil of "good" vs "evil" but a little more complicated. Raskolnikov is portrayed as selfish and cunning, but intelligent, using the ends to justify the means. Razumihin is Raskolnikov's friend, but he is very honest as well as completely positive. He acts selflessly and tries to help others, though he isn't the brightest, and his good will often ends in him being taken advantage of. This is a classic contrast which I often experience in my own life; there are the intelligent ones who often aren't the most charitable, but often make out with better situations for themselves/are never made a fool of or taken advantage of, and there are the hopelessly selfless who often find themselves being used, but are always loved and fairly satisfied.
Dunia vs Luzhin (Pyotr Petrovich)
This is an interesting case. Luzhin is a senator or a lawyer, something along those lines, and quite rich. He eventually reveals to Dunia that his dream is to marry a beautiful, intelligent, but poor girl, as a poor girl would always be indebted to him and would do anything he wished/be completely subservient. Dunia, however, is her own woman and has respect for herself, and does not go along with Luzhin's plans. Luzhin is later shown to be selfish, petty, and just a general jerk.
Dunia instead finds love with a man who respects her, Razumihin.
Well those are some basic character analyses, hope you enjoyed this series on Crime and Punishment. Try reading it yourself! It's a pretty good book :)