Literary commentators have sometimes analyzed the differences in style between Pope and Swift by alluding to the Latin poets upon whom they modeled their work. Pope, we are often told, patterned his style after Horace, and Swift, after Juvenal. This observation implies that Pope's satire, like Horace's, is relatively light-hearted and gentle, while Swift's, like that of Juvenal, is much more acerbic and angry.
There is some truth in this, but unfortunately for most of us who do not read Latin (including myself), it's difficult to judge how close in style and technique the two English poets are to their ancient models. Before we talk about style per se, it's probably a good idea to look at the genres Pope and Swift used. Pope, except for the prose prefaces to some of his works, wrote exclusively poetry. Swift did write poetry, but almost all of it consists of occasional pieces and jeux d'esprit which do not represent him at his best. His major satires are in prose, the most important being the novel-like Gulliver's Travels and shorter pieces such as A Modest Proposal and the now much less read Tale of a Tub and Battle of the Books.
If we look at the style of all these works, it's true that Pope's The Rape of the Lock, probably his most widely read work today, does not express the kind of anger and bitterness that Swift's satires generally exhibit. Both A Modest Proposal and Book IV of Gulliver's Travels have a shocking intensity in their condemnation of, in the former, the English ruling class and its insensitivity to the Irish, and in the latter, mankind in general, who are depicted as the savage, animal-like Yahoos ruled over by intelligent, benevolent horses. In Gulliver's Travels Swift implies that humans, judged by their behavior, are in reality more beast-like than animals are. None of Pope's satires make this kind of scathing, slashing attack, except perhaps for The Dunciad, in which Pope ruthlessly derides his enemies in the literary world, especially the playwright Colley Cibber. The Dunciad, however, shows us a more fundamental difference between Pope and Swift. Pope's satires are aimed at specific people and their behavior. In The Dunciad, he attacks incompetent writers. In The Rape of the Lock, the vanity and superficiality of the upper classes are his target. Swift, on the other hand, has a broader target: human nature in general.
Partly because of this, many commentators have judged Swift's satire to be more universal in its implications than that of Pope or others of the neoclassical period, such as Pope's predecessor Dryden. However, Swift's very intensity and negativity raise another issue. Satire, as some commentators have defined it, is a genre which holds folly up to ridicule but simultaneously at least implies that there is, or should be, a positive opposite to the negative side of human nature. This is the view of the early twentieth-century critic F.R. Leavis, who in an essay on Swift acknowledges that Swift is a great writer, but asserts that his greatness consists only in the force of his attacks, and not in their effectiveness as satire. If a writer seemingly denigrates everyone or everything, his work, Leavis implies, is merely a kind of invective and is not true satire. Probably no one could credibly make this assertion about Pope. In understanding the nature of Pope's and Swift's work and the differences between them, you might also take a look at the poetry or prose of other satiric writers of the eighteenth century, such as Samuel Johnson's "The Vanity of Human Wishes" and Voltaire's Candide. These writers knew the work of Pope and Swift well, but of the two, you might ask who was the more influential upon Johnson and Voltaire, or upon other writers who followed them?
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.