I think the difference is that Jews and Christians believe that women are equal before God, always. That “man shall leave his father and his mother, and be joined to his wife; and they shall become one flesh” as it says in Genesis.
That depends on what you mean by "Jews and Christians believe that women are equal before God." You probably need to define what the phrase "equal before God" means. Equal in what? The word equal is definitely a loaded word these days and one must be very clear what they mean when they use it. (You are probably right, but your statement may be interpreted in different ways.) The sentiment expressed in the above statement may also be anachronistic, taking the values of today as the values of long ago.
The people who make up Judaism and Christianity today are very,very culturally different than the ones who lived 2000 years ago. Ancient Judaism did not believe that men and women share the same social rights and responsibilities before God, even if they did believe that men and women were equally valued by God. (If you know of any source, that explicitly states that women and men are equally valued by God, please let me know, I think it would be pretty interesting. The man and woman becoming one flesh scripture that you mentioned does not say that man and woman are equal, just that the woman and the man are one flesh...man was apparently dominant in this relationship in the minds of the ancients. This is why Jewish men were allowed to divorce their wives unilaterally, but not the other way around. Early Christians also inherited these views, as St. Paul makes very clear in several of his epistles when he calls man the head of the woman etc.
Christianity also did not believe that men and women shared the same social roles and responsibilities as men. Nevertheless, Christianity elevated the status of women beyond what other religions had done, because Christianity uniquely said that marriage was indissoluble. Therefore, a man could not cast off his wife on a whim. Also Christianity completely rejected polygamy, which elevated woman's social status. Despite these difference,however, men and women still did not have the exact same social rights and responsibilities though there was a certain degree of overlap since most of the commandments of God apply equally to men and women.
Giving different roles, expectations, and responsibilities to men and women means by definition that men and women are some how different from each other and therefore are not equal in some ways. Men and women are not equal, they are complementary would be a better way of describing man and woman's relationship with each other. (After all, the word equal means the "same" and we all know that men and women are not exactly the same). However, even if men and women have different roles, responsibilities, etc. this does not mean that God values men and women any differently than each other, and I think that it is obvious that women were esteemed in early Christianity as being "precious to God", and equally precious at that, though I don't know if the word "equal" is ever explicitly used in any ancient texts to say this.