The end results of these two satirical poems are very different as a result of somewhat different techniques. In de Souza's "Catholic Mother," the dominant techniques are contrast and contradiction, surprise, and silent oppositional opinion. In Swift's "Beautiful Nymph," the dominant techniques are ironic contrast, step-by-step ironic description, ironic effects.
The irony in Swift's poem begins with the title. While expecting the story of a beautiful nymph, a goddess of Earth personifying the purity of nature, what is offered is, one might say, the ironic deconstruction of a nymph. Swift offers the description of the hard reality of an even harder life that only defers death from deprivation. Swift's descriptive technique is one of the three ancient Greek descriptive methods that specifies description must begin at the head and work down through every physical point to the very toes.
Chaucer famously used this method in his popular (though perhaps annoying) description of the Wife of Bath in the “General Prologue” of The Canterbury Tales. However, Swift's implementation of this descriptive method turns it ironically upside down in order to shock readers into realization of the horrific truth he is exposing. As Swift describes each descending physical point, he disintegrates Corinna’s beauty, personhood, health, and hope. He ends on the painful note of the effect associating with her has on other people: they are egregiously nauseated and poisoned.
But how shall I describe her Arts
To recollect the scatter'd Parts?
Or shew the Anguish, Toil, and Pain,
Of gath'ring up herself again? 
The bashful Muse will never bear
In such a Scene to interfere.
Corinna in the Morning dizen'd,
Who sees, will spew; who smells, be poison'd.
De Souza's more subtle though still disturbing poem, starts out with a contrast between the title and the initial text of the poem. The tile is "Catholic Mother," yet the first lines are, "Father X. D’Souza / Father of the year." In fact, in the whole of the first two stanzas, the mother behind Father X. D’Souza's "One Big Happy Family" is only alluded to in "we’ve had seven children" and "Lovely Catholic Family." This silence relating to the mother not only contrasts with but contradicts the title as does the emphasis on Father X. D’Souza, though it is his award: "Here he is top left / the one smiling."
Both the surprise and the silent oppositional opinion come in the last two lines, structurally set apart as they are, when the Catholic mother finally enters the picture. Her sudden, unheralded appearance is one surprise, her silence is another, “says nothing.” The ironic reintroduction of the pillar idiom of the second stanza, "Pillar of the Church / says the parish priest," into the last stanza's short, informal line, with no capitalization, "the pillar's wife," subtly asserts the mother's silent opposition to being the means by which Father X. became Father of the Year. It also subjects the proclaimed happiness and provision of the first stanza to doubt and contradiction.
Pillar of the Church
says the parish priest
Lovely Catholic Family
says Mother Superior
the pillar’s wife