Since both are masters of the heroic couplet, both scathing satirists, how, it might be asked, does Dryden achieve effects quite foreign to Pope? In what respects does Dryden offer something that is other than what Pope offers–something distinctly his own?
To answer, consider some lines from a poem, “The Hind and the Panther” that even Dryden’s fervent admirers might concede to stretch the sympathies of modern readers. In the passage, the “fable” tells of various Christian sects and denominations; the “Lion” is James II, guarding England from the wolfish Scottish calvinists among others–whom the Muse disdains the name:
More pow’rful, and as vigilant as they,
The Lion awfully forbids the prey.
Their range repressed, though pinched with famine sore,
They stand aloof and tremble at his roar;
Much is their hunger, but their fear is more.
These are the chief; the number o’er the rest,
And stand like Adam naming every beast,
Were weary work; now will the muse describe
A slimy-born and sun-begotten tribe,
Who, far from steeples and their sacred sound,
In fields their sullen conventicles found:
These gross, half-animated lumps I leave,
Nor can I think what thoughts they can conceive.
But if they think at all, ’tis sure no high’r
Than matter put in motion may aspire.
Souls that can scarce ferment their mass of clay,
So drossy, so divisible are they
As would but serve pure bodies for allay:
Such souls as shards produce, such beetle things
As only buzz to heav’n with evening wings,
Strike in the dark, offending but by chance,
Such are the blindfold blows of ignorance.
The lines represent an extreme against which the world, in Dryden’s imagination, often threatens to fail: a degradation, grotesque, violent, and debased of life and matter itself–something that would be captured by the sublime style. But Dryden does not attempt a full Sublime: instead, he gives us the Sublime from a distance, the potential horrors of existence seen and felt from the safer middle course that his poetry steers.
Pope, we might say, is no stranger to the Sublime. Take “The Dunciad.” But Pope, the master of the miniature, shrinks the objects and notions that make up the scenes of sublimity in that poem: even their immensity becomes his plaything. It may not be the best, but it is an example. It is from Book 2:
This labour past, by Bridewell all descend,
(As morning prayer, and flagellation end)
To where Fleet-ditch with disemboguing streams
Rolls the large tribute of dead dogs to Thames,
The king of dikes! than whom no sluice of mud
With deeper sable blots the silver flood.
‘Here strip, my children! here at once leap in,
Here prove who best can dash through thick and thin,
And who the most in love of dirt excel,
Or dark dexterity of groping well.
Who flings most filth, and wide pollutes around
The stream, be his the weekly journals bound;
A pig of lead to him who dives the best;
A peck of coals a-piece shall glad the rest.’
In naked majesty Oldmixon stands,
And, Milo-like, surveys his arms and hands;
Then sighing, thus, ‘And am I now threescore?
Ah why, ye gods! should two and two make four?’
He said, and climb’d a stranded lighter’s height,
Shot to the black abyss, and plunged downright.
The senior’s judgment all the crowd admire,
Who but to sink the deeper, rose the higher.
And Book 4:
And now had Fame’s posterior Trumpet blown,
And all the Nations summon’d to the Throne.
The young, the old, who feel her inward sway,
One instinct seizes, and transports away.
None need a guide, by sure Attraction led, 
And strong impulsive gravity of Head:
None want a place, for all their Centre found,
Hung to the Goddess, and coher’d around.
Not closer, orb in orb, conglob’d are seen
The buzzing Bees about their dusky Queen. 
The gath’ring number, as it moves along,
Involves a vast involuntary throng,
Who gently drawn, and struggling less and less,
Roll in her Vortex, and her pow’r confess.
Not those alone who passive own her laws, 
But who, weak rebels, more advance her cause.
Whate’er of dunce in College or in Town
Sneers at another, in toupee or gown;
Whate’er of mungril no one class admits,
A wit with dunces, and a dunce with wits. 
It is not a knock against Pope to say that these lines work because he is horrified by the disorder and chaos of the world–but that it is a chaos and disorder wholly accommodated to his poetry in so far as, even in the most dramatic paradoxes of dulness and wit, the destabilizing of dark and light, solid and phantasmal, Pope can maintain a grasp of proportion and never cedes his authority to impose relations, even if the relations he imposes (dark/light; dulness/wit) are aimed at undermining the established dichotomies, so that we can no longer hold fast to distinctions of sense.
Pope, that is, remains always a master of magnitude, so that everything can be reduced to a human scale. The effects are terrific: human depravity, stupidity, ridiculousness can be expressed in terms of the entire universe. But the sublime is also always potentially contained within the scale and scope of human life.
Dryden, when he approaches the sublime, does just that: approaches. He does not attempt to apprehend, master, or impose himself upon the vast chaos of the universe, any more than the figures in his poetry do. It is, implicitly, a statement about the human function of poetry in a universe that exceeds the powers of poetry to describe. The lines are rimed and rimmed with the sublime, terrible or noble, but do not claim to be of it.
But Dryden’s great moment come when the poetry allows us enough of a sense of the horrors and confusion, the universal, supra-human confusion, to believe that no further approach could be warranted.
Perhaps this is why Dryden was so well suited to translate the Aeneid, whereas Pope was so well suited for Homer’s Iliad. The stature of the heroes in Homer’s epic is achieved by a diminution of the gods, as well as by an elevation of man; and they are, even when the gods sit in Olympus, of recognizable human proportions. But that intensifies, rather than diminishes, the intensity of the action; it could be said that, whatever role the gods play, it is a poem about what man can make of man, what man can be to man–of man as objectifying, brutal, warped, heroic, on a scale of man itself. Pope understood that scale well; he could apply it to the entire ‘chain of being’ (it is difficult to imagine Dryden writing “Essay on Man” in part because the upper and lower reaches of the ladder he would not feel, I think, comfortable subordinating to poetic argument).
In the Aeneid, although the gods play a role, the moving forces are immense, beyond the control of even the gods: History, the sadness of the world, Fate, a universe that even the Gods cannot understand. Aeneas’ dignity, the poem’s melancholy, its despair or its optimism, are measured against these; but they are of a scale that is unutterably greater than human life. The fortitude and virtue require to endure them is the subject matter of the poem; the fortitude and virtue required to endure man is the subject matter of the Iliad. That is probably too glib a way of putting it, but it serves to at least draw a provisional contrast. And Dryden’s style, embodying as it does, both fortitude and virtue, capable also (as it is not often though to be) of plaintive notes and vulnerability, distinctly answers that poem’s demand; that it does so answer tells us something about the strength of Dryden’s original poetry, too.
From his corporally sturdy vantage point, he apprehends forces that move the world and human life in the world, and that, even when they are most intimately human in their issue and expression, exceed human agency, volition, and accounting. Hence the success of his translation of Lucretius:
Nor when the youthful pair more closely join,
When hands in hands they lock, and thighs in thighs they twine,
Just in the raging foam of full desire,
When both press on, both murmur, both expire,
They gripe, they squeeze, their humid tongues they dart,
As each would force their way to t’other heart;
In vain; they only cruise about the coast,
For bodies cannot piece, nor be in bodies lost,
As sure they strive to be, when both engage
In that tumultuous momentary rage,
So tangled in the notes of love they lie,
Till man dissolves in that excess of joy.
The prospect of bliss and terror of man’s dissolution into something greater or lesser, but always other, than man–that gives Dryden’s verse its “tumultuous momentary rage,” and allows it the show of strength that is the regained composure of a couplet closing.