The Jewish and Christian understanding of the Adam and Eve story are vastly different. The Jewish one is positive while the Christian one is negative. Here's the difference.

In Judaism after God creates Adam and Eve they live in the Garden of Eden understood as "paradise" which is an "island" of tranquility while all around it is the chaos of the untamed world. They are one with God but as they were created by God do not have the knowledge of God. This is forbidden to them and this dividing line is metaphorically illustrated by the fruit of the Tree of Knowledge of which they are forbidden to eat. Eve is tempted by the serpent which is the metaphor for disobedience to the will of God and by eating the fruit she is disobedient to God. Eve convinces Adam to eat of the fruit and he is also disobedient to God. Eve is not blamed for inducing Adam to eat the fruit because the decision to do so is his alone and thus the act of disobedience is also his alone. Adam and Eve are ashamed of their disobedience, discover their nakedness, and nakedness is the metaphor used to illustrate their shame for being disobedient to God. God punishes both Adam and Eve for their individual decision to be disobedient by expelling them from the Garden of Eden.

The Jewish exegesis of these events is also vastly different than that of Christianity. In Judaism the metaphor of nakedness is necessary because Adam and Eve must become aware of their sexuality, their maleness and femaleness, so that when they are expelled into the world they will have sexual desire and reproduce. The obvious question is, "Why does God expel them from the Garden of Eden instead of a lesser punishment?" The Jewish answer according to Rabbi Joseph Telushkin etalii is that it was God's intention when he created them that they would end up in the world to both populate and subdue it. This is another reason Eve is not blamed for inducing Adam to eat the fruit of the Tree of Knowledge: she was playing the role ordained for her by God.

As an aside this is exactly the same premise for understanding the betrayal by Judas of Jesus in the Gospel of Judas; that is, Judas was playing the role given him by God without which the Passion of our Lord, and our salvation, would not have been possible by the death and resurrection of Jesus. As an aside I read the Gospel of Judas when it was finally published last year and was pleased to discover that this late First or early Second Century gospel’s understanding of Judas cites the same conclusion I came to when I wrote, The Historical Jesus: Man, Myth or God. The difference between the two is that the Gospel of Judas is considered a Gnostic Gospel and my argument was from Thomas Aquinas’ Summa Theologica.

The Jewish understanding of the story was largely accepted by Christianity until Augustine in the late 400s. Below is an excerpt from my book titled, Rights, Liberties, and Social Justice: How the Fight Over Abortion, Homosexuality, Intelligent Design, nd Poverty Created American Fascism and Destroyed the Separation Between Church and State due out in early 2008.

“In the late 400s a Roman named Jovinian wrote a treatise which no longer survives in which he argued that the married state was superior to virginity. Augustine wasted no time in writing his first treatise against Jovinian, De Bono Conjugali (On the Good of Marriage), which he followed with De Virginitate (Of Holy Virginity).  Augustine makes it clear in the second chapter of De Bono Conjugali that virginity is the more holy state and that procreation by sexual intercourse is secondary to death and death is the consequence of sin.  He substantiates this by citing Genesis I: 28:

And God blessed them, and God said to them, 'Be fruitful and multiply, and fill the earth and subdue it   (RSV, Genesis 1:28)

In doing so Augustine's argument is that at this point in the story of Genesis, Adam and Eve having committed no sin, are immortal and just as God was able to create them without benefit of sexual intercourse, create Jesus in a virgin womb, and bestow on bees progeny without sexual intercourse, humanity would be generated by,

an advance of mind and abundance of virtue as it is set in the Psalm, 'Thou shall multiply me in my soul by virtue' (Augustine, De Bono Conjugali, p. 2)

Thus for Augustine it is sin that deserves the condition of death and there can be no sexual intercourse without our mortality which makes sexual intercourse a secondary good to virginity even when the product of that good is children.

Augustine goes on to say very clearly that there is a hierarchy of permissible sexual intercourse within marriage.  At the top of the hierarchy and if the partners are able to do so without committing fornication or adultery, is that they should maintain marital celibacy. Consequently, the only time they should engage in sexual intercourse is when the purpose is to beget a child.  Although not stated in De Bono Conjugali, commentators cite other works that by this Augustine means that during such intercourse the partners' thoughts and feelings should remain fixed on the child to be conceived, they should derive no sensual pleasure from the experience, and they should wait to see if pregnancy occurs before trying again.  In the second level of the hierarchy if one of the partners is so filled with lust that they are in danger of committing adultery it is the duty (the marriage due) of the other partner to have sexual intercourse even if they do not need to do so to satisfy their own lust.  This is the due and mutual service of marriage that Augustine often speaks of.  However, all sexual intercourse committed within both the first and second level of the hierarchy is a venial sin and must be confessed prior to reception of the Holy Eucharist as one would not be in a state of grace with this sin on his or her conscience.   The third level of the hierarchy is when one partner feels lustful and simply "wants sex" and demands the other partner comply.  At this level there is no issue of being on the brink of adultery.  In Augustine's mind this is purely sex for the sake of sex.  Therefore it is a mortal sin, a sin of life and death, a sin that puts one's soul in jeopardy headed toward Hell.

Augustine's view of intercourse is that it is,

The very case of the more immoderate requirement of the due of the flesh, which the Apostle [Paul] enjoins not on them by way of command, but allows to them by way of leave, that they have intercourse also beside the cause of begetting children; although evil habits impel them to such intercourse, yet marriage guards them from adultery or fornication.  For neither is that committed because of marriage, but is pardoned because of marriage.  It is in a way a mutual service of sustaining one another's weakness in order to shun unlawful intercourse; so that, although perpetual continence be pleasing to one of them, he may not, save with consent of the other.   (Augustine, De Bono Conjugali, p. 4)

Augustine continues,

For intercourse of marriage for the sake of begetting hath not fault; but for the satisfying of lust, but yet with husband or wife, by reason of the faith of the bed, it hath venial fault: but adultery or fornication hath deadly fault, and, through this, continence from all intercourse is indeed better even than the intercourse of marriage itself, which takes place for the sake of begetting.  But because that continence is of larger desert, but it pay the due of marriage is no crime, but to demand it beyond the necessity of begetting is a venial fault, but to commit fornication or adultery is a crime to be punished; charity of the married ought to beware, lest whilst it seek for itself occasion of larger honor, to do that for its partner which cause condemnation.  (Augustine, De Bono Conjugali, p. 5)

We can now place the Christian understanding of the Adam and Eve story as well as Augustine's negative view of women into perspective. Unlike the Jewish understanding where the events of the story are seen as metaphor, Augustine chooses a literal understanding of the events. Tthere are two major differences between the Jewish exegesis of the story and Augustine's. The first is that for Augustine the total responsibility for Adam and Eve's disobedience to God rests on Eve's shoulders. The second is that the punishment for Eve's disobedience is not expulsion from the Garden of Eden. It is the discovery of human sexuality, lust, and the necessity of sexual intercourse for procreation.

So, in Augustine's understanding of the story why does God expel Adam and Eve from the Garden of Eden? The answer is not because they were disobedient but because of their knowledge of their sexuality, lust, and the necessity of procreation they are no longer "pure" as God created them but have "defiled" themselves. Thus, by their defilement they are no longer able to be a part of God's perfect creation (the Garden of Eden) but must enter the world of chaos; that is, the world of defilement.

Consequently, for Augustine, Original Sin enters God's creation in the persons of Adam and Eve as they are now in a state of defilement due to the stain of their sexuality, lust, and need to procreate. By the act of sexual intercourse that results in pregnancy they transmit to their progeny for all eternity the taint of Original Sin.

Thus, the positive Jewish exegesis of the story (doing the will of God) is changed by Augustine to a negative exegesis (Original Sin). For Augustine, Original Sin is the consequence of Eve's disobedience and his subsequent condemnation of all women. However, that statement is an oversimplification as Augustine's critique of women was greatly influenced by his theological understanding of the Virgin Mary, the value of virginity vs. marriage, and how it is possible for a woman to gain salvation which is directly linked to his theology of Mary, virginity, and marriage.