Nietzsche - crime, sin and punishments

Question

Deleuze in Nietzsche and Philosophy wrote:

In comparison with Christianity the Greeks are children. Their way of depreciating existence, their 'nihilism', does not have the perfection of the Christian way. They judged existence blameworthy but they had not yet invented the refinement which consists in judging it faulty and responsible.

When the Greeks spoke of existence as criminal and 'hubric' they thought the gods had driven men mad; existence is blameworthy but it is the gods who take upon themselves the responsibility of the fault.

In Christian Catholic theology, it is God in the person of Jesus that takes on the sins of mankind; at least in my understanding. How does this differ from the gods 'who take upon themselves the responsibility of the fault'? Even if different in degree, a certain affinity seems to be admitted.

This is the great difference between the Greek interpretation of crime and the Christian interpretation of sin. This is the reason why, in the Birth of Tragedy, Nietzsche still believed in the criminal character of existence, since the crime at least didn't imply the responsibility of the criminal.

Sin is different from crime: how? Is one a crime against God and his order; and the other a crime against Man (say a king, or a state) and his order?

'Foolishness','folly', a little 'disturbance in the head', this much even the Greeks of the strongest, bravest age conceded of themselves as the reason for much that was calamitous - foolishness, not sin! did you grasp that?

...'he must have been deluded by a god', they concluded finally, shaking their heads...in this way the gods in those days served as originators of evil - in those days they took upon themselves not the punishment, but what is nobler, the guilt (GM II)

Fault is transformed into guilt.

Deleuze pushes along further to recognise an affinity:

All that is needed is a change of sex, Eve instead of the Titans, a change in the gods, a single God and actor and lover of justice, in place of the spectator-gods and 'olympian judges'.

He assigns this 'whittling down of a great difference' to Nietzsche; but provides no textual justification - what evidence is there that suggests that N did indeed come to this realisation?

Or is Deleuze distilling a new concept by completing what Nietzsche has set in motion here?

Its worth noting tht the etymology of the word sin reveals:

Old English synn "moral wrongdoing, injury, mischief, enmity, feud, guilt, crime, offense against God, misdeed," ... probably ultimately "it is true," i.e. "the sin is real" (compare Gothic sonjis, Old Norse sannr "true"), from PIE *snt-ya-, a collective form from *es-ont- "becoming," present participle of root *es- "to be"

Answer 1

There seem to be several questions here, I'll address the first and second:

I'm not a Deleuze scholar but his claim seems fairly clear from the quote. In the Greek system, according to D, when people commit crimes, the blame is shifted to the gods. In Christian belief, on the other hand, people are responsible for their own sins, but Jesus takes the punishment for those upon Himself, although blameless.

D is indeed drawing parallels between the systems, but he nevertheless does consider this itself to be a psychologically significant shift. To provide a simplified gloss of his claims: In the Greek system, you bear the punishment, which is the consequence of your crime, but you don't bear the guilt. In the Christian system, you bear the guilt, which is the consequence of your sin, but not the punishment. The crime is something that you do, an event that happens. Sin is something that comes from within you, an intrinsic flaw in your nature.

I won't venture to evaluate whether he is correctly evaluating the Greeks, the Christians or Nietzsche, but I do think this at least represents a reasonable distillation of the provided quotes.