There is an ocean of difference between Paine and Bradford. The two men epitomize the different beliefs of their age, though Paine was a bit radical even by the standards of his period.
Bradford was a traditional Puritan. He believed in the literal truth of Scripture (ex. the world literally being created in seven days, Adam and Eve as actual people and not archetypes, etc.). For him, the colonies in America were an ideal way to practice what he and the Puritans believed were a purer form of Christianity. He also believed in the concept of divine providence, that God had a hand in what happened at the colony.
Paine was a deist, as in a person who believed in a creator/higher power but not in the truth of organized religion. In fact, Paine was critical of how religious leaders suppressed questioning any dogma, even if said dogma conflicted with sense or science. He also did not believe Jesus of Nazareth was actually God, but simply a wise man following the will of God. He admired Jesus but had little use for organized Christianity or even the Bible itself, which he considered a violent, hateful work written more by man than God. For him, the United States should be a place where people could worship and believe whatever form of religion they pleased.