There are two forms of the rhetorical device of satire. One is named for the Roman poet satirist Horace who wrote in Latin; his satire is gently mocking and humorously cajoling in the hopes of inspiring a return to a higher standard for whomever or whatever he was satirizing. The second is named for the Roman poet satirist Juvenal also writing in Latin; his satire is distinguished by a contemptuous and indignant tone that employs harshness and realism to incite a return to a higher standard for whomever or whatever he was viciously attacking and satirizing. The distinguishing feature of the two is therefore tone and intent: Horatian satire has a mild smiling voice of indulgent wit that inspires improvement while Juvenalian satire has an indignant contemptuous tone of chastisement and harsh ridicule that is meant to incite reform.
Pope is an excellent example of the first style: of mild, indulgent, smiling Horatian satire. Pope's most famous satire is The Rape of the Lock. In it he reduces social foibles to amusing poetic banter with the hope of bringing order and a return of sensible living to a social situation gotten out of hand. His tool is humorous witty banter that exposes absurdities and follies.
Swift is an excellent example of the second style: of harsh, contemptuous Juvenalian satire. Some of Swift's more famous satires are Gulliver's Travels and "A Modest Proposal." It is particularly evident in "A Modest Proposal" that Swift's vein of satire falls to the bitter, cutting Juvenalian satire that is so different from the mild, gentle Horatian satire of Pope. In "A Modest Proposal," Swift tries to be (and succeeds at being) shocking and outrageous in his suggestions and statements. For instance, he suggests that there are individuals in Ireland that would be properly used for food.
Therefore the final comparison of the overall similarity and difference between the satire of Pope and Swift is that while Pope is a mild-mannered, gentle Horatian satirist, Swift is a vulture-manned, indignant Juvenalian satirist, which is a style that can be used to good purpose when and where the need arises for it.