Both Swift and Goldsmith criticized the hard-heartedness of British society's treatment of the poor. Swift, however, criticized the lack of compassion with harsh, biting satire. For example, the narrator of "A Modest Proposal" proposes that the starving Irish fatten and sell their year-old babies to rich English lords in Ireland as gourmet table delicacies, since the English refuse to help the Irish in any other way. This kind of social criticism was shocking—and continues to shock to this day. It uses a negative example to make its point: nobody would want to be like the clueless narrator who was so inhumane as to recommend cannibalism as a solution to the problem of poverty. This negative example, Swift hoped, would encourage sensible people to devise more humane solutions to human suffering.
Goldsmith, in contrast, is much more gently humorous in his social critique. In his "The Character of the Man in Black," he shows how much more our deeds matter than our words by using the positive example of the Man in Black. The Man in Black speaks harshly about the poor as "impostors" who should be jailed, but he actually models positive behavior by helping them out in their time of need. We can hear the gentleness of Goldsmith's prose in this passage:
...an old man, who still had about him the remnants of tattered finery, implored our compassion. He assured us that he was no common beggar, but forced into the shameful profession to support a dying wife and five hungry children. Being prepossessed against such falsehoods, his story had not the least influence upon me; but it was quite otherwise with the Man in Black: I could see it visibly operate upon his countenance, and effectually interrupt his harangue.
I could easily perceive, that his heart burned to relieve the five starving children, but he seemed ashamed to discover his weakness to me. While he thus hesitated between compassion and pride, I pretended to look another way, and he seized this opportunity of giving the poor petitioner a piece of silver, bidding him at the same time, in order that I should hear, go work for his bread, and not tease passengers with such impertinent falsehoods for the future.
In contrast, Swift does not spare us harshness in "A Modest Proposal," writing:
I have been assured by a very knowing American of my acquaintance in London, that a young healthy child well nursed, is, at a year old, a most delicious nourishing and wholesome food, whether stewed, roasted, baked, or boiled...
While Oliver Goldsmith and Jonathan Swift were both satirists, they targeted different aspects of society in their works. Goldsmith, like Swift, mocks the society of his day, but his depiction of characters hinges on their representing types of people. They do not appear to the reader to be individuals in their own right - a method other writers such as Moliere uses. As such, much of Goldsmith's satirical focus is on society as a whole. In addition, unlike much of Swift's satirical work, one of Goldsmith's primary motivations was to make people laugh, often making his ridicule more subtle and easier for the reader to swallow. The gentle nature of Goldsmith's satire is puzzling, because it is often difficult to discern what is truly sentimental and what is truly satirical.
Jonathan Swift, on the other hand, does not run up against the same problem. In his works, his readers become very aware of Swift's satirical targets. In "A Modest Proposal"(1729) perhaps the most well-known of Swift's satires outside of Gulliver's Travels (1726), he targets not only the Irish who are lazy and apathetic toward their own lives but also the English who have put the Irish in such a situation. The very subject matter of the pamphlet alerts the reader to the nature of the work. Gulliver's Travels, like "A Modest Proposal," targets more specific aspects of society than much of Goldsmith's works. In his novel, Swift takes the scientific community to task, as well as humanity as a whole. As such, his satirical work tends to be much more pointed in drawing out its targets and more stinging in his indictment of them.
They are both satirists of social issues which they wrote in their stories as mockery of the snobbery, hypocrisy and falsehood of the upper classes, especially those who are "in charge" of society.
Goldsmith has personified characters with characteristics that you would think are meant to evoke respect and love for the character only to find out that he was mocking the character and evoking laughter in the reader. Swift does the same in Oliver Twist, for instance, where he particularly pounds on the Laputians, who are the representation of all that is wrong in being human.
The contrast is mainly their focus. Swift is more of a humanist=-- he criticizes society from the point of view of how man has ruined himself, and society along with it. Goldsmith is more of a social observer, and writes and mocks about it as a whole.