Even if it's already two weeks since your question, I'd still like to answer. As Shalom already pointed out, there is as of yet, no unified opinion in Halacha (orthodox Jewish religious law) regarding embryo donations and also egg donations. In Halacha, the religious status of a child (if it is considered Jewish or non-Jewish) depends only on the mother. In the case of embryo- and egg donations there are, so to speak, two mothers involved: the egg or embryo donor and the woman who carries out the pregnancy and gives birth.
The three basic opinions in the halachic discussion are therefore 1) The woman who donated the embryo or egg is the mother 2) the woman who gave birth to the child is the mother 3) both are mothers to the child. Which position is given preference depends on which Rabbi you ask. However, there seems to be a trend shifting from the older position (No. 2) to positions No. 1 and No. 3. As you can see, it will be difficult to get a clear answer regarding whether the child is Jewish or not - different Rabbis in different places will view this differently.
For the child, this uncertainty could make finding his or her identity rather complicated. There is another issue as well: Assuming that the child is halachically Jewish, he or she would be obligated by Jewish Law to follow Jewish religious customs, such as keeping kosher and Shabbat and many more. In a non-Jewish household that is extremely difficult. (I'm speaking from experience - was born non-Jewish but in my teenage years got interested in Judaism and started trying to live as a religious Jew while still with my parents - it led to quite some trouble. I've converted to Judaism since and live now in Israel.)
Aside from practical considerations, Judaism in general discourages Jewish children growing up in non-Jewish families, because the child might very well identify with the religion of his or her adoptive parents and then, from the strictly Jewish standpoint, be lost to Judaism and a "sinner" (though it is of course not the child's fault as he or she couldn't choose how and where to be raised). Therefore it seems to be the better option to choose an embryo from a non-Jewish woman in order to avoid all of these issues. (By the way, the child still could convert to Judaism later in life, without all these complications, if he or she is interested ;-)
I would like to recommend visiting the website of Machon Puah. They are a well-known institution in the United States and in Israel and research all kinds of questions involving fertility treatments and Jewish law.If you contact them, they might be able to give you more information.