How can I compare and contrast the images, tone, and theme of the poems "My Last Duchess" by Robert Browning and "Richard Cory" by Edwin Arlington Robinson?

While both Browning and Robinson write of human relationships, these relationships in "My Last Duchess" and "Richard Cory" display more differences than they do similarities.
IMAGES
In Robert Browning's "My Last Duchess," the Duke pulls open a curtain behind which he keeps hidden a portrait of his late wife. He equates art and experience as he declares, 

"That's my last Duchess painted on the wall,Looking as if she were alive."

He speaks of the painting of his wife in words that objectify her.
In a similar manner, the presence of Richard Cory when he appears in the town is objectified; he is viewed from a distance and considered as less a person than a superior being of royal bearing:

Whenever Richard Cory went downtown, We people on the pavement looked at him.He was a gentleman from sole to crown,Clean favored, and imperially slim.

In Browning's poem, the image of a curtain creates a division between the portrait and its owner. This division suggests that the disdainful Duke became infuriated by his "smiling" wife, whose friendly attitude toward others (including admiring men) led him to cruel action against her. There is also a socio-economic class difference between Richard Cory and the townspeople, who are but "on the pavement" and must look up at him. This difference creates a divide between the two classes of people, as well, but ironically, it is the lower class who are less accepting in Robinson's verse.
Another difference that exists is that the viewing of the painting of "My Last Duchess" is a private screening (along with the pretentious display of the bronze Neptune taming a seahorse), whereas Richard Cory displays himself publicly without pretension. Nevertheless, Cory is seen more as an object of envy (as the Duke also perceives himself) than as a person with whom to speak.

And he was rich--yes, richer than a king--...In fine, we thought that he was everything

Interestingly, the mention of friendliness certainly elicits different tones in the two poems under discussion here. Whereas the haughty Duke has punished his too-friendly wife for her friendliness--"all smiles stopped together"--the townspeople appreciate Richard Cory's cordiality:

...he fluttered pulses when he said,"Good morning"....

TONE
Browning's dramatic monologue spoken by the Duke has a subtle tone that reveals his faults. For instance, as the Duke displays the portrait of the "last duchess," there is in his monologue an undercurrent of his possessiveness that discloses his suppressed jealousy and anger. There is a cruelty to the Duke's tone. In fact, he seems completely unconcerned that another prospective duchess might have misgivings about accepting the "gift" of his name. He is absolutely confident and points to his bronze Neptune (who, like him, tames those in his possession).
This tone produces an impression on the reader of a certain repulsion for him. There is also an awareness of his possessive and controlling personality.
In contrast to the insolence of the Duke, Richard Cory's actions reveal that he is truly a gentleman:

   ...admirably schooled in every grace:In fine, we thought that he was everything   To make us wish that we were in his place. 

Ironically, however, Richard Cory does not draw himself any closer to his audience than does the arrogant Duke, although for different reasons. For while the townspeople generate an admiring tone as they speak of Cory, the class difference acts a barrier of feeling that produces the tragic end of the alienated and desperately lonely Richard Cory, altering the tone to one of shock.
THEMES
One common theme of both poems is that of communication. However, whereas the Duke perceives open and honest communication as compromising to his power, Richard Cory strives to communicate honestly by being polite and greeting people and being "human when he talked."
Another theme that is shared by both poems is that of perspective. The Duke's version of reality is near-sighted and selfishly produced. His arrogance leads him to eliminate all that interferes with his proud name and sense of superiority. Like the Duke, the common people of "Richard Cory" have a distorted perspective of the gentleman Richard Cory, and they fail to recognize his agonized separateness from them; they see only his fine clothes and "glittering" walk. They believe he is different from them when in actuality he shares the same need for human contact and warmth. 
Still another theme is pride. Even though Richard Cory's pride is a genuine conscientiousness in maintaining his appearance and good manners, ironically this diligence serves only to alienate him from the "people on the pavement."