Both poems suggest an ideological condition of the subjugation and objectification of women. "A Suttee" describes the practice of a bride immolating (burning) herself on her husband's funeral pyre. This is an ancient practice which has been almost universally banned. Unfortunately, it does still occur, with cases cited in India. The practice suggests that women are not fit to live without their husbands, as if it is unchaste or as if they are just unable to cope with the loss. The practice of suttee has not been equal in terms of gender; in the documented cases of sati (suttee), there are little to no examples of male suttee. Clearly, this is a horrific double standard.
"My Last Duchess" is obviously less violent, but the Duke literally objectifies his wife with the painting on the wall. Not there to defend herself, the Duke, having no respect for his dead wife, implies she was promiscuous ("she liked whate'er/ She looked on, and her looks went everywhere.") Then he literally tells the man, whose master's daughter he is about to marry, that she is his object.
The Count your master's known munificence
Is ample warrant that no just pretense
Of mine for dowry will be disallowed;
Though his fair daughter's self, as I avowed
At starting is my object.
In "A Suttee," the majority of the poem describes the bride's beauty, again as if she is nothing more than a pretty object. The poem ends on a morbidly ironic note. That they will be united, "no more to part" almost sounds romantic, but that romanticization is part of this deplorable ideology of the woman being subservient to the man in body and spirit.