Both Bunyan and Swift were deeply religious men whose work satirizes what they consider ignorance, vanity and prejudice. They lived in very different circumstances though, and their style reflects those differences.
Bunyan was a lower-middle class nonconformist, with little education, whose work reflects the vernacular tradition of the morality play. His writing is deeply and overtly religious, and The Pilgrim's Progress uses the plain language of dissenting preaching. His satire is directed generically against the worldly and sinful, and generally is simple and direct, addressing universal issues, and giving it a broad appeal.
Although Jonathan Swift had suffered a certain degree of poverty in childhood due to his father's death, he was a well-educated member of the professional (upper middle) class, educated at Trinity College, Dublin and well versed in classical learning. He was a member of the Established Church, eventually becoming Dean of St. Patrick's Cathedral, and an associate of the Tory William Temple, a defender of the value of classical learning. Swift's satire is heavily influenced by Latin models, especially Juvenal, and more distinctly individuated than Bunyan's, with many thinly veiled topical and political references. His language is more ornate and rhetorical, with a more varied and Latinate vocabulary. Rather than condemning vice in broad strokes, he is focused on specific political controversies of his own period. His work is more indirect and allusive in style, and also uses broader earthy humor and even slapstick.