The purpose of Plymouth Plantation was to document and describe the progress of the pilgrims as they tried to build a community so far from their homes and it also went on to celebrate in some ways the liberty and freedom from the home country's rule. It also had a great deal of focus on the Christian nature of the colony and the ideals they espoused and some negative descriptions of other groups who did not adhere as tightly to those same ideals.
Common Sense, on the other hand, was addressed to a different audience and its purpose was to stir up sentiment against England by pointing out that the English could not provide the rights and liberty that they claimed to because of the situation that the colonies were in along with their great geographical separation from England.
The difference between the two is that Common Sense was clearly designed to encourage separation from the British while Plymouth Plantation was designed to celebrate the democratic ideal but not by driving a wedge between England and the colonies.
As the two answers above imply, Bradford's Of Plymouth Plantation (1620-1650; 1856) and Paine's Common Sense (1776) have little in common, but they represent important documents in the history of what became the United States. Because the authors' purposes and audience were vastly different, there are more contrasts than comparisons.
Bradford, who became the leader of the Mayflower colony for several decades after their arrival in 1620, wanted to lay out in great detail how and why the Puritans decided to leave England for the wilds of America and, equally important, what their experience was in the first few decades in America. Bradford's account is pure historical writing, couched in the language of the Puritan belief system, designed to explain the Puritans' persecution in England, their exile in Holland, and, ultimately, their success in America. We find, for example, a number of letters detailing conflict among the Puritans themselves and their attempts to find a place where they could exercise their religion without persecution. That Bradford is interested primarily is the truth of the Puritan experience is evident in his introduction:
. . . I must begin at the very root and rise of the same. The wyche I shall endeavor to manifest in plaine stile, with singuler regard trueth in all thynges. . . .
From a stylistic standpoint, then, even though we are reading the English of the early 17thC., Bradford is careful to cover his history in a straightforward and relatively "plaine" style--that is, wherever he can, he avoids heavily latinate diction common among learned writers at the time. Writing in a plain style is something he has in common with Thomas Paine.
Unlike Bradford in Of Plymouth Plantation, whose goal was to record the history of a people, Paine's purpose in Common Sense is not to write an exhaustive history of a group of people but to motivate American colonists to take action against what Paine considered to be an abusive government in Great Britain. Although Paine wrote with a sense of history, he concentrated his efforts on the history of the British government and monarchy, so his goal was not history-as-history but history-as-motivator for taking action against the British parliament and monarchy.
The common denominator in the two works is in their style--both men wrote in what is considered the plain style for their respective periods. Bradford's style is characterized by an adherence to Anglo-Saxon vocabulary where he can, and, typical of Paine's 18thC. plain style, although his diction is latinate, his typical sentence structure is considered less convoluted than other essayists of his period--Johnson, Swift, Pope, for example.