Compare Browning's "My Last Duchess" and Eliot's "The Love Song of J. Alfred Prufrock."
Browning's "My Last Duchess" and Eliot's "The Love Song of J. Alfred Prufrock" are similar in both presenting unmarried, middle-aged men suffering from insecurity as they explain their actions to a third party. However, they differ greatly elsewhere.
The narrator of Browning's poem is an aristocrat with "a nine hundred year old name," arrogant and haughty. His insecurity shows in his loquacity. At first, he seems merely prissy and insufferable. Later, as it becomes clear that he has had his former wife executed for real or imagined flirting of the most harmless nature ("then all smiles stopped together"), he becomes a textbook example of what has been called "the banality of evil," with his offhand admission followed quickly by talk of another marriage.
The narrator of "Prufrock" lives at a middle level and has wasted much of his life in pointless socializing, "measured out my life with coffee spoons." Instead of evil potency, he admits "am not Prince Hamlet, nor was meant to be.... almost, at times, the Fool." He can catch a glimpse of ideals, "have seen them riding on the waves," but this only accentuates his feelings of uselessness.
The shared theme would seem to be the need for both self-awareness and action. The duke, who can act, is sunk in a lethal and banal shallowness; Prufrock, who is capable of sustained reflection, is paralyzed when it comes to action.
Both of these poems also deal with male/female relationships. The duke in Browning's poem demonstrates a dominant attitude over women. He is dissatisfied with his duchess because she is a flirt, and because she gives attention to many men, and doesn't reserve all her attention for him. It "was not her husband's presence only" that caused her to blush with joy. The duke was too controlling to allow that - she was his property and must behave as he instructs. But she would not be "lessoned" as he felt she should. Browning demonstrates the subservience of women in his poem.
Eliot, however, gives women the edge. For poor Prufrock, women have the power. They are able to entice and to scare him. They are able to direct the course of a relationship. Prufrock wishes to push a relationship forward, but he hesitates - he is scared to be brushed aside by a women who would say "that is not what I meant at all." There is an indirect suggestion here that these women are, at the very least friendly, at the most flirtatious. However, where as Browning's duke looks to control that, Eliot's man is intimidated by it. Women have moved up in society by the time of Eliot's composition.