They both have a feeling of endurance and fortitude. Both poems are from the viewpoint of a mother, or of a strong black woman who has gone through a lot of trials. In "The Negro Mother" those trials are stated outright:
"I am the child they stole from the sand...
I am the woman who worked in the field...
I am the one who labored as a slave,
Beaten and mistreated for the work that I gave--
Children sold away from me, husband sold, too.
No safety, no love, no respect was I due."
Yet, despite this, and many other trials that she lists off throughout the course of the poem, there is a message that if you endure, work hard, and have hope, it will all turn out well. She states, "God put a dream like steel in my soul," and "I had to keep on! No stopping for me--" and "I nourished the dream that nothing could smother" and " Believe in the right, let none push you back." So although the poem lists many depressing circumstances, there is a feeling of hope and strength.
In "Mother to Son" she lists her trials metaphorically, as a hard staircase that she's had to climb that
"had tacks in it, /And splinters,/ And boards all torn up, /And places with no carpet on the floor,"
but that she has kept climbing them, even when it's been hard. And she counsels her son to "don't you turn back." So the same message and feeling of strength and fortitude is felt in that poem too.