When comparing "My Last Duchess" by Robert Browning with "A Suttee" by Letitia Elizabeth Landon, to what extent is each poem, and the story each tells, gendered?
To clarify your question somewhat, what you are asking is to what degree these poems are or are not gendered: heavily gendered or lightly gendered. Asking about "each poem" separately from the "story" of each is a bit ambiguous. One might say each poem is heavily gendered because each author discusses a heavily gendered theme. In "Suttee" Landon talks about the act of a widow's death on her husband's funeral fire. In "Duchess" Browning talks about the idea of a woman's male dependence. The gendering Browning exposes might be said to be a protest against the idea of a woman's male dependence. In this sense, each poem is heavily gendered.
If you separate the stories told from the poetic form that houses them, then each story is also heavily gendered. Browning's is the story of a Duke and Duchess. The Duke is so disgusted that her looks and joy are not confined to him alone that he commands she find joy in only him and smile at only him. She dies at his command (though Browning gives no clear hint of the Duke having any direct responsibility in her death).
This story is heavily gendered as it expresses the patriarchal female stereotype of the mindless, emotional and irrational woman who has no moral character nor any noble virtue. Browning's satiric wit and a tone of disdain debunk (ridicule) this gendered idea as the Duke puts the Duchess's death, his next dowry (price received for taking the bride), and a "sea-horse" all in one breath, so to speak:
There she stands
As if alive. Will 't please you rise? ...
The Count your master's known munificence
Is ample warrant that no just pretence
Of mine for dowry will be disallowed;
Notice Neptune, though,
Taming a sea-horse, thought a rarity, ...
Landon's story is the story of a bride and widow. The beginning of the lady's story encompasses the end. The lady, celebrated in her right, becomes the bride whose identity becomes subsumed by (meshed with, buried by) the identity of the male, and she will end, though living, when he ends.
And yet the crowd that gather at her side
Are pale, and every gazer holds his breath.
... for the bride ...
She gives [away] the gems that she will wear no more; ...
The red pile blazes--let the bride ascend, ...
The heavy gender bias is revealed in the title "A Suttee," an act of sacrifice so a woman whose husband has died will not become a scorned widow who has failed in her duties. The story is gender biased toward the patriarchal male presumptions about the life of woman: it is worthless without the sanction of a man's life giving it his worth. The bias can be summarized like this: She exists for his pleasure and when he can no longer receive pleasure from her in death, she will cease existing on his funeral pyre ("the red pile blazes").
Both stories are heavily gender biased. Both give a similar message that male dominance based on patriarchal presuppositions is deadly: deadly for the woman and deadly wrong.