This is an excellent question. To answer it, we first need to make sure we're identifying the terms involved: abolitionist and feminist.
An abolitionist was a person who sought to end the practice of slavery. These individuals didn't always agree on the details, but they did when it came to the big picture. Some wanted African slaves to be emancipated and made citizens of the United States with full rights. Some wanted emancipation with limited rights and citizenship. Some thought the former slaves should move to other countries where they would be more accepted, and some wanted to found colonies in Africa that would be composed primarily of former slaves.
In the end, though, this was a group of men and women who wanted to end a practice that they thought was unchristian and horrible. The abolitionist movement was about ending slavery and not necessarily about creating an equal station for former slaves (though, of course, many abolitionists argued for just that.) The interesting component of this is that such a movement has a fairly defined goal that can be measured. Either slavery exists or it doesn't. When it doesn't, the movement can end.
Feminists, on the other hand, are individuals who campaign for women to have rights that are equal to those of men. This is a goal that is much harder to measure, though "victories" can be seen in areas such as politics, economics, and sports. Feminism, unlike abolitionism, does not necessarily have a clearly defined end-point.
As far as overlap:
- Both are (or were) movements dedicated to empowering a specific societal demographic that was being discriminated against.
- Both sought to use the political process as a means to do this.
- Both groups used public rallies to raise awareness.
- Both groups used independent publications to sway opinion.
- Both groups were composed of both men and women and included members of all races.
- Both made progress slowly.
- Both groups had an important component of striving for economic equality.
- Both groups faced massive resistance.
As far as areas that don't overlap:
- The abolitionist movement, for all real purposes, is no longer around while feminists still are
- The slaves were not themselves in a position to agitate for their own rights. It required "outsiders" such as whites and free blacks to fight for them, while feminists were better able to advocate for themselves.
- The abolitionist movement resulted in a great deal of violence and bloodshed, largely absent from the feminist cause.
- While the goal of eliminating slavery is accomplished with one piece of enforceable legislation, eliminating gender inequality is much more complicated.
Interestingly enough, many women were very prominent members of the abolitionist movement at a time when women were not encouraged to have strong opinions. Perhaps some of this energy and experience in defeating the evils of slavery helped those "founding mothers" to begin a movement to liberate themselves from a defacto "domestic slavery."
Probably feminism began in London, England when Elizabeth Katie Stanton met her friend; Lucretia Mott, the Quaker abolitionist at the International Anti-Slavery Convention in the spring of 1840 while Stanton traveled on her honeymoon. The male delegates voted that women should be denied participation in the proceedings, even if they, like Mott, had been nominated to serve as official delegates of their respective abolitionist societies. The men voted to require the women to sit in a roped-off section hidden from the view of the men in attendance.
The humiliation of this experience must have focused Mott’s and Stanton’s attention on suffrage for women and resulted in the birth of feminism.