the opera, Richard Cory at a show,
And the rumor of his parties and the orgies on his yacht!
Oh! He surely must be happy, with everything he's got.

This adds a Citizen-Kane-like element regarding the hypocrisy and amorality of the rich to the story. The repetitions in the verse, typical of the pop-song format, include ones concerning the speaker's own life of struggle and poverty. This intensifies the contrast between Cory and the ordinary people, those who work in his factory. Robinson's sparse commentary on this point is limited to two lines:

So on we worked and waited for the light,
And went without the meat and cursed the bread . . .

This does not make explicit the connection between the speaker and Cory himself, who is actually the speaker's employer in the song. The last significant difference between Robinson's and Simon's treatments is that in the song, after we are told that Cory has shot himself, the speaker repeats his statement that

Oh I wish that I could be
Richard Cory.

This carries with it the grim irony that the speaker wishes to be Cory because of his wealth and life of privilege, but after Cory's death, he still wishes to be like him—in other words, to be dead.

In summary, Simon gives us a restatement of the basic meaning of Robinson's poem, but it is an expanded one in which added emphasis is placed on the speaker's personal feelings. Simon stresses as well the similarity between the speaker and Cory—the human condition of suffering in spite of differences in economic status and class—which is more understated in Robinson's poem.

Both the poem and the song are among my favorites, and fully worth re-reading or listening to again.  I encourage you to come up with a more detailed analysis, but I will help you get started with context comparison.

First of all, the subect of both the poem and the song lyrics is the same person, Richard Cory.  He is well known around town, wealthy, respected, and envied.  The speaker is the same as well, as both are told from a first-person point-of-view.  Both end in the same dramatic irony with the man who seemed to have everything committing suicide.

The biggest differences between the poem and the song lyrics is the song lyrics are more detailed.  It is almost as if the song gives the story behind the poem.  Notice the refrain of the song, "I work in his factory."  The speaker here is not just one of the many people in the town who has hears of or sees Richard Cory on a regular basis.  It is a man who works for Richard Cory.  The song lyrics do not suggest a personal relationship (factory work is hardly personal), however, the speaker has a bit more credibility in the song.  The song also goes into more detail about Richard Cory.  Everything is contextually relevant, and sounds like it could be true based on the few clues from the poem.

I think that the song is angrier than the poem.  The poem's tone creates an almost reverential quality to Richard Cory.  It creates the sensibility that Richard Cory's superiority lies in his wealth.  The fact that the speaker of the poem is poor is separate from this reality.  The song creates a different vision of wealth.  The elements are still the same, but the chorus of the speaker working in one of Cory's factory creates the impression that the speaker's poverty is the trade off for Cory's wealth.  This is where there is anger and not so much as reverence.  The almost parasitic relationship present helps to accentuate the anger felt by the speaker, for while Cory enjoys his "orgies on his yacht" (great line) the speaker works in a factory and toils for his existence.  In the end, when Cory puts a bullet in his head, the chorus is the same, almost suggesting that death is a preferable existence to being poor.  This helps to bring out the anger the speaker feels about his predicament and the state of Richard Cory, something that is not as present in Robinson's poem.

Simon and Garfunkel's song "Richard Cory," written in 1965 and recorded on their second album The Sounds of Silence, portrays Richard Cory as "a banker's only child" who not only is wealthy, but has political connections.  He has "everything that a man could want:  power, grace, and style."  In Edward Arlington Robinson's poem, however, Richard Cory is not portrayed as powerful politically or otherwise; he is simply "richer than a king."  There is also no knowledge by the "people on the pavement" of what he does.  But, in the song, the singer works in his factory and tells about seeing Richard Cory's picture on the society page as well as the rumors of "his parites and the orgies on his yacht."  He is not quite the distant, isolated, elevated "imperially slim" vision that the poem presents although the people who work in the factory only see him in the photos on the society page.

The Richard Cory of the song is a rich and powerful man surrounded by other wealty people whereas the Richard Cory of the poem is simply wealthy, rich like a king and never seen with anyone else.  He appears in town and says "Hello," but there is no apparent socialization that occurs.  Robinson's Cory seems much more isolated from human contact; his separation from the ordinary people seems more apparent as they look up from "the pavement" to this "imperially slim" man who is always alone.