How would you compare and contrast the poems "America" by Claude Mckay and "The New Colossus" by Emma Lazarus?

Let’s start with a quick overview of the two poets in question.
Emma Lazarus (1849–1887) was born into a wealthy Jewish family in New York City. As a young poet, she became aware of anti-Semitic prejudice through reading (rather than through personal experience), and in the 1880s she became one of the most prominent writers decrying the persecution of Russian Jews. She also wrote about the plight of poor Jews in the US and other countries, and became one of the earliest Zionists. In 1883, Lazarus wrote “The New Colossus” to help raise funds to build a pedestal for the Statue of Liberty.
Claude McKay (1889-1948) was a prolific writer of poetry, novels, and short stories, all exploring issues related to racism in his native Jamaica, the US, and elsewhere. He was concerned with its political and social aspects, but also with the internal emotional and intellectual processes by which a human being can defend his or her human dignity in the face of discrimination. One of the earliest influences on McKay’s thinking was the German philosopher Arthur Schopenhauer. Schopenhauer believed life was inevitably painful. He argued the best human beings can do is develop their spiritual and emotional lives by creating art and preserving their sense of justice and morality.
We can see Lazarus and McKay had several characteristics in common. Both belonged to groups that suffered widespread discrimination. While both were deeply concerned with racism and prejudice, they also both had the advantage of childhoods free of persecution and violence, allowing them a chance to use their intelligence and become highly educated.
Both “America" and "The New Colossus" are sonnets exploring the experience of refugees and minorities in the United States. Each is built around a duality—that is, a pair of contrasting ideas that generate tension. In "The New Colossus,” this duality is expressed through the structure of the verse itself. This is an Italian sonnet: fourteen lines divided into an octave (the first 8 lines) followed by a sestet (the final 6 lines). The rhyme scheme looks like this:
ABBCACCB (the octave)DEDEDE (the sestet.)
Like most Italian sonnets, “America” examines two ideas or perspectives: the first in the octave, and the second in the sestet. (This is the duality mentioned above.) Lazarus begins by describing the “new Colossus,” Lady Liberty, who is to replace the warlike Colossus of antiquity. Instead of a conquering masculine force, she will be a nurturing feminine one: the “Mother of Exiles”. The octave is hopeful and idealistic, employing gentle imagery like “sea-washed, sunset gates” and the lady’s “world-wide welcome,” “her mild eyes” commanding the harbor.
At the end of the eighth line comes the turning-point (sometimes called the volta, Italian for “turn”) into the new perspective of the sestet. Here, Lazarus has Lady Liberty herself describe the plight of poor immigrants to the US:

                              . . . your tired, your poor,Your huddled masses yearning to breathe free,The wretched refuse of your teeming shore.

In the final two lines, Lazarus confirms her conviction that these refugees will be welcomed and cared for in their new country:

Send these, the homeless, tempest-tost to me,I lift my lamp beside the golden door!

McKay’s “America,” by contrast, is a Shakespearean sonnet. (As a child, McKay loved Shakespeare and the English Romantic poets, and his earliest writings were attempts to emulate them.) Here, too, we see a duality: the tension between love for his adopted country and rage against it. Unlike “The New Colossus,” “America” expresses those conflicting emotions not through poetic structure, but through the language itself. (If he were writing a traditional Shakespearean sonnet, one idea would dominate the first twelve lines, and the second one would appear in the final two lines.) McKay shifts perspective over and over, sometimes within a single line (e.g., “Giving me strength erect against her hate . . .”)
We see this in the first quatrain:

Although she feeds me bread of bitterness,And sinks into my throat her tiger’s tooth,Stealing my breath of life, I will confessI love this cultured hell that tests my youth.

Although America feeds him bitterness, pierces his throat like a predator, and tries to kill him, McKay says he loves the “cultured hell” that brings out his own greatest strengths as he fights to defend himself against it.
Because “America” is written in the first person, we feel McKay’s struggle with US culture is more intimate and personal than Lazarus’s in “The New Colossus.” McKay is not talking about immigrants in the abstract, but about his own experience as a black newcomer.
McKay’s feelings about the US remain conflicted to the end of the poem; unlike Lazarus, he gives us no clear conclusion in his final couplet. These last two ambiguous lines remind us again of his love for Shakespeare, whose own sonnets frequently mention Time and decay:

Beneath the touch of Time’s unerring hand,Like priceless treasures sinking in the sand.
https://daily.jstor.org/emma-lazarus-golem/