Because John Winthrop delivered so many different sermons, I am going to assume you are referring to his most famous one, "A Model of Christian Charity," and the most famous of John Robinson’s letters, his "Farewell Letter." Both of these men were spiritual leaders of the fledgling Puritan community, and their writings demonstrated the attempt to maintain harmony within that community according to the Christian virtue.
Winthrop’s sermon situates the moral imperative of the Puritan Christian community within the divine grace of God. That is to say, he argues that all members have the responsibility to uphold good relations with one another, but this responsibility is only made possible because God allows it. In his third reason for God’s disposal of mankind, Winthrop says,
“Thirdly, that every man might have need of others, and from hence they might be all knit more nearly together in the bonds of brotherly affection.”
Winthrop gave this sermon while travelling to the New World on the Arbella, while he and his congregation were en route to settle the Massachusetts Bay Colony. This statement reflects the general expectations Winthrop had of the Puritans, based both in the Christian ethic as well as the pragmatic necessities of settling an unchartered territory. It was critical that the Puritan settlers maintain peace within their own community, as the hardships the New World had to offer could not have been overcome if members consistently bickered amongst one another.
John Robinson’s farewell letter is also a Christian moral tract intended to cultivate equanimity within the Puritan community. More than anything else, Robinson called on his fellow Congregationalists to avoid taking offense from one another, and to maintain harmonious relationships with one another. For example, he says,
“And for that, watchfulness must be had that we neither at all in ourselves do give, no, nor easily take offense being given by others.”
Both Winthrop and Robinson’s writing was meant as an admonition to those Puritans who were going out to create a new, model Christian community. The survival of this community was deeply predicated on a solidarity between all the members who made it up, their cooperation, and goodwill toward one another. The primary difference between these two writings may be that Winthrop saw such unanimity as a divine gift of God’s grace, whereas Robinson put more responsibility on the individual.