The answer to the question is "Neither." Woman is not the woe of man, sin is.

When God created man, in the sense of mankind, he created "Adam." Adam was a creature whose inner man was made in the spiritual image of God while his outward man was that of a human being who was obedient to God; both Adam's outer and inner man where of one flesh in God.

When Adam, because he was of the flesh, was no longer able, due to the weakness of the flesh, to maintain, in both his inner and outer man, the spiritual image of God, he fell away from God into a deep death-like sleep. Although he had not as yet sinned, having fallen away from God, he was still weaken as to temptation and as a result no longer fully one with His Maker.

God realizing Adam's weakened state needed to separate the things of the Spirit (God) from the things of the flesh, as God can not have sin in His presence. So while Adam "slept," God took of the flesh his rib and created "wo(e)man." But the "wo(e)man" that was created was not a female human being per se, as the term "woman" refers to today. It fact, the "wo(e)man" God created was entirely a creature of the flesh that was opposite and unlike God in that it was characterized by the potential for sin and the "woe" that would befall it as a result of betraying God.

In other words, the "wo(e)man" was a creature of the flesh through whom the offense to God would come and the consequences thereof would be suffered. This state of misery, as a result of sin, was indicated by the word "woeman." The word "woe" being subsequently shortened to "wo" and hence "woeman" became "woman" and with shortening it, the word's confusion with a similarly written word, but not with the same meaning; the similarly spelled word being "woman," meaning a female human being.

Referring to the wo(e)man with the word "Eve," further exasperated the term's confusion with women in general because "Eve" is usually taken to be a female name rather than a term meaning the "mother of life;" a term which in Scripture is used to distinguish the mother which gives birth to life in the flesh, which is sin, from the mother which gives birth to life in the Spirit, which is God. The sinful nature of the "wo(e)man" was subsequently revealed in the Book of Genesis when "Eve," because of the weakness of the flesh, offended God choosing sin over obedience unto the fall of Adam and as a consequence, "Eve" became the way through which the "woe", the curse of God, came upon all those who are born of the flesh as opposed to the Spirit.