There are many similarities between these two struggles. Let us look at two of the more important ones.
First, both struggles took place over a very long period of time. The women's rights movement in the United States dates back to at least the 1840s and is still continuing (though at somewhat lower intensity than at some other points) today. The "formal" struggle for black rights began with the rise of abolitionism in the 1830s and has also continued to the present. In both cases, there have been times of greater (like the 1960s and '70s) and lesser intensity of action.
Second, both struggles have involved a mix of strategies. In both cases, legal action has been used to advance the cause. However, both movements have also used things like direct action and protest as tactics.
One major difference between the two is that the movement for black rights had much more widespread approval among its constituency. Of course there were disputes as to tactics and timing, but there was little or no sense within the black community that there was no need to push for more rights. This is much more present among women as a whole in the US, with many (typically conservative) women pushing back against the idea of what others see as full equality for women.
First, one should note that these two struggles overlap, as roughly half of all African Americans are women and approximately 13 percent of all women in the US are African American.
In both cases, legal inequality and discrimination existed for centuries, but even with the gradual removal of legal discrimination, great inequalities remain.
Although both women and African Americans have the right to vote, there is some evidence of voter suppression efforts even in the past decade as well as gerrymandering intended to suppress minority votes, something that would not apply to female non-minority voters.
In the 114th Congress, roughly 20 percent of members are female and 8.7 percent black, meaning that women are slightly more underrepresented than black people, though both groups remain underrepresented.
Both groups struggle against a white male patriarchy and suffer from lower wages and less access to positions of power than white men. On the other hand, much of the feminist movement was middle class and women as a group have substantially more net wealth than African Americans as a group; women are more likely to have university educations and advanced degrees.
In the case of both groups, there has always been the issue of whether their struggles have been for admission to the elite white male power structure or a more radical transformation of society.