Much of Anne Bradstreet's work was written during the years when she was raising her many children, and so often she takes her family as her main subject, though we certainly see elements of her Puritan struggles with sin and frailty in the texts as well. The poems provide evidence of her own piety and desire to be and do good on earth as well as her profound romantic love for her husband.
In "Deliverance from a Fit of Fainting," for example, Bradstreet addresses her God and asks that he give her strength so that she may be worthy of praising him. She had, evidently, fainted and experienced it as a kind of death. She insists that God revived her "feeble spirit" and banished her doubts, restoring her to life, and she asserts that she now only lives to praise God.
In "To My Dear and Loving Husband," Bradstreet declares...
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that, "If ever two were one, then surely we. / If ever man were loved by wife, then thee." She uses metaphors to describe how much his love means to her—it is worth "more than whole mines of gold"—and how hers flows on and on, like unstoppable "rivers." She hopes that they can continue to love one another like this in life so that they "may live ever" after death with one another.
Phillis Wheatley, unlike the aristocratic Bradstreet, was an enslaved person, stolen from her home in West Africa around the age of seven. Being quite frail, she was sold to a wealthy family to work in their home, but the Wheatleys realized her intelligence and taught her to read and write. Many of her poems are elegies written to commemorate and memorialize and praise some deceased person, like the Reverend George Whitefield, a prominent and popular preacher at the time.
However, she comments on slavery, Christianity, revolutionary patriotism, and more, even employing allusions to mythologies and legends as well as the Bible, showing her breadth of knowledge as well as the depth of her analytical skills. The poem she wrote for George Washington, "His Excellency General Washington," is an especially good example of this.
Both Anne Bradstreet and Phyllis Wheatley were poets born elsewhere. Bradstreet was from England and Wheatley from West Africa. While they had drastically different personal freedoms in the context of the New World, they both made poignant commentaries on the nascent nation and its ties to the rest of the world.
Consider Bradstreet's poem "A Dialogue Between Old England and New." The poem oscillates between the speaker's observations on England and New England, in North America. In the last passage of the poem, the speaker proclaims:
And shall I not on them wish Mero’s curse
That help thee not with prayers, arms, and purse?
And for my self, let miseries abound
If mindless of thy state I e’er be found.
Essentially, the poet acknowledges the complexity and tremendous amount of need to fully form New England. In these lines, she asserts that everyone should be willing to contribute towards progress. New Englanders should stay aware and involved, including the poet, who wishes "miseries abound" on herself should she neglect this duty.
Wheatley was kidnapped and forced into slavery, and her poems were often used (or rather, exploited) by Abolitionists for the anti-slavery agenda. In her poem "On Being Brought from Africa to America," she reflects on the place of black people in this land. She acknowledges the extreme irony of being forced to contribute to a place under the yoke of slavery, yet she does not necessarily reject the idea. She compels the reader to "Remember, Christians, Negros, black as Cain, / May be refin'd, and join th' angelic train." Like Bradstreet, she views the New World as barrelling towards a complex future, in which all people should actively take part. Especially, she believes that black members of society should also be permitted to "join th' angelic train" of progress.
In short, both poets characterize the New World as a complex place in need of tremendous collective work, but overall a place which could be capable of progress. Acting on this potential is a core theme in early American literature, and both poets significantly helped proliferate this idea through their writing.
I'm certainly no expert on either Phillis Wheatley or Anne Bradstreet, but I have read several selections by each of them. As I see no one else has answered your question, I'll share my observations and hope you find them helpful. Bradstreet's work is a little older than Wheatley's, and it was written as private work which was never intended to be published. Her poetry was primarily personal in terms of content--devotional/spiritual and emotional reflections. Her work is structured formally (as in clear rhyming patterns and rhythms) and there are few surprises poetically in her work. Instead, we read the simple, straightforward reflections of a woman who loves God, her husband, and her home.
Wheatley, on the other hand, is a much more sophisticated poet. While Bradstreet was a devout believer and early settler in America, Wheatley was a black woman who had clearly been given some formal educational training. She uses many allusions (references to things outside the literature), including mythology and the Bible. Her work is not all particularly patterned (again, I don't claim to have read all her work, so take that into account) or rhymed. Her poetry is more lyrical and full of imagery than Bradstreet's, and her subject matter is more connected to her circumstances in life as a black woman brought from Africa to America.
Both women reflect on spiritual themes (for example, Bradstreet thanks God even when her house burns down, and Wheatley expresses her thankfulness to God for letting her come to America).
I wish I had more, but that should at least get you thinking about the selections you've read and will prompt some new ideas about which you can reflect.