For example: The "Work of Christ", climaxing in the suffering and death, is, among other things, to enable men to quit being vicious. It's not just throwing away virtue for vice (which is her most misleading formulation in the quoted passage). It is the shattering of what traps people in vice, in moral inferiority, and in the consequent misery.
Those Christians who deny that humans are ever more than "counted" as good,but instead are freed and enabled to become - if not good - better than they were, might have trouble distinguishing what they think from what she says. But Catholics and the Orthodox would not recognize their belief in her account of it.
And the contrast between sacrifice or service and happiness is, to us, bogus. The life of virtue, while it can lead to opposition, suffering, and even death, is considered a life "toward" happiness and strength, toward excellence. The cartoon image of the devil on one shoulder and the angel on the other is wrong if the devil is supposed to be offering enjoyment and self-actualization and the angel suffering and self-abnegation.
For us, to redeem that cartoon, we'd insist that the devil is lying and that following his suggestion will tend to make one weak and unhappy. Following the angel's advice will, we think, make one happier and stronger.
I think possibly Rand mistook the anemic and moralistic version of Christianity promoted by some who are uncomfortable with any sort of pleasure or ease for the solid, vital, even uproariously delighted religion which proclaims (Psalm 16, verse 11) that at God's right hand are pleasures for evermore.
I can't even remember the name of the Rand book I read. But I was struck that the first romantic encounter was about domination, indeed almost rape. Another poster has suggested that it's hard to see where family duties (and desires) fall in her scheme. What could be one's duty to the elderly and infirm in her views?
Of course, a scheme which postulates atheism and denies heaven (and, I suppose, hell) will not envision the sort of human excellence which we talk about. In such a case, it's hard to imagine what difference her thought makes. If a stronger group advocating a different view wiped her teaching from the face of the earth, what would she think of that, I wonder.
This is not meant to be any kind of refutation, except of her depiction of Christianity. I'm not saying she's wrong to say the Christians are wrong (though I think so). I'm only saying the I don't think Christianity is what she says it is -- which I think was what you were asking for.
Ummm, hmmm,... Ayn Rand was a Jewish immigrant...
The fatal flaw of Ayn Rand's philosophy: Morality and all of those associated ideals are rooted entirely in a presupposition that some higher power defines what is correct for human behavior.