Women who have abortions aren't sadistic freaks who like killing "babies". If we are given the choice to transfer the embryo to an artificial womb instead of abortion, then of course we would choose it. So it would be more about the pro-lifers--if they don't want to allow artificial wombs when it's an option, then they HAVE to agree to allowing abortions. Their argument right now is that "even fetuses have rights" (though apparently grown women don't). If they were to say no to artificial wombs for whatever reason, then their current argument would be invalid and they'd have to allow abortions or else come up with whatever other reason it is that women shouldn't have full human rights during the time they're pregnant. The only thing I can think of is religion, which obviously wouldn't be legal if they actually used the term as they'd be forced to do. "Life begins at conception"--how is that an argument against artificial wombs? The life would still be preserved, except it'd be inside an uncaring fake womb, instead of an unwilling female slave. Of course, whilst the abortion issue would be solved, artificial wombs could open up whole other cans of worms, such as insurance companies not paying for natural births because they'd be "riskier" than artificial womb births--the same bs they do now with home births.
The prevailing argument regarding abortion debate isn't something as simple as "reproductive rights". The prevailing debate is whether life begins at conception. Now, how artificial wombs throw this debate for a whirl is that feminists can argue day and night about the right to not be pregnant, "pro-choice" as it where, but they will never be able to justify the now needless killing of the infant in the process. Once the child is removed from the womb, and as such no longer her problem, there is indeed no reason for the child to not be kept safe, be birthed, and ultimately adopted. If the pro-life side can adopt this "lesser evil", the entire abortion debate will be effectively resolved.
I see almost no downside to artificial wombs. If a woman decides that she does not want to have a child even though she is already pregnant, she can just transfer the fetus into the artificial womb and everybody wins. No fetuses were aborted, and no woman had to have an unwanted birth. The child could just be adopted later after it is born. There is, however, a small downside. Religious people will always find a problem with this because they are going to believe that it will "remove a bond between the mother and the child", even though that makes no sense considering that adopted children have the same bond with their mother as biological children. Artificial wombs will also be a huge bonus to feminism, since women will no longer be told to aspire to motherhood, since they could just have the womb do that for them.
The abortion controversy is mostly in regards to the religious view that life starts at conception. It doesn't matter if that life is growing in a woman or an artificial womb. To the religious, life is a life no matter what stage it is the moment sperm meets and fertilizes egg. To the none religious that disagree with abortion, they maybe more subdued because of the grounds that you wouldn't create life in this artificial womb, unless, it was planned for someone or something.
Truth be told, you will probably get anther side in this fight that says artificial wombs are dangerous or unnatural to an extreme that man shouldn't be playing God.
Even if artificial wombs solve the current problem of abortion controversy, only more strife will rise out of new issues presented by the new technology of artificial wombs. For example, some might see an artificial womb as an inhumane disconnect from the mother. There will most likely be many more other unforeseen issues that will become apparent only after the technology advances enough and it is time for our society to face the possibilities. But no matter what, people will always manage to generate an argue against something that is new and "scary" to them.
Artificial wombs have the potential to be a great service in clarifying the debate. For some abortion opponents (and I dare say most or all supporters), they will resolve the issue by allowing unwanted fetuses to be brought to term and adopted by people who want them. However, a sizable number of abortion opponents will not be swayed, because the real issue for them is women's sexuality. Those who want to control women will continue to oppose this innovation because, in their view, "women should not be able to have sex without consequences." The sexual revolution and the ability of women to control their bodies and to make independent decisions about their lives is intolerable to this segment of our population. Fortunately for the rest of us, the artificial womb will help reveal the real underlying issue in their world view.
Artificial wombs will definitely provide greater reproductive choices to a great many people, and will allow religious pregnant women and other pregnant women who don't wish to 'kill' the fetuses growing inside of them greater freedom in the matter. This isn't the real issue though; that would be the twofold 'life begins at conception' idea and the fact that many 'pro-lifers' don't really give two craps about the infants involved and just want their dogmatic, narrow-minded view of the world to be agreed to by everyone else. Artificial wombs would give the pro-choice side of the abortion debate more credibility, but honestly would probably be seen as some sort of unnatural monstrosity by at least a sizable minority of the pro-life side.