I was looking through the other entries in this thread to date, and surprisingly I don't see the quote that is probably THE most important quote relevant to the connection between Nietzsche and Epicurus - section 58 of AntiChrist:

Der Antichrist 58.

In point of fact, the end for which one lies makes a great difference: whether one preserves thereby or destroys. There is a perfect likeness between Christian and anarchist: their object, their instinct, points only toward destruction. One need only turn to history for a proof of this: there it appears with appalling distinctness. We have just studied a code of religious legislation whose object it was to convert the conditions which cause life to flourish into an "eternal" social organization,—Christianity found its mission in putting an end to such an organization, because life flourished under it. There the benefits that reason had produced during long ages of experiment and insecurity were applied to the most remote uses, and an effort was made to bring in a harvest that should be as large, as rich and as complete as possible; here, on the contrary, the harvest is blighted overnight… That which stood there aere perennis, the imperium Romanum, the most magnificent form of organization under difficult conditions that has ever been achieved, and compared to which everything before it and after it appears as patchwork, bungling, dilletantism—those holy anarchists made it a matter of "piety" to destroy "the world", which is to say, the imperium Romanum, so that in the end not a stone stood upon another—and even Germans and other such louts were able to become its masters… The Christian and the anarchist: both are decadents; both are incapable of any act that is not disintegrating, poisonous, degenerating, blood-sucking; both have an instinct of mortal hatred of everything that stands up, and is great, and has durability, and promises life a future… Christianity was the vampire of the imperium Romanum,—overnight it destroyed the vast achievement of the Romans: the conquest of the soil for a great culture that could await its time.

Can it be that this fact is not yet understood? The imperium Romanum that we know, and that the history of the Roman provinces teaches us to know better and better,—this most admirable of all works of art in the grand manner was merely the beginning, and the structure to follow was not to prove its worth for thousands of years. To this day, nothing on a like scale sub specie aeterni has been brought into being, or even dreamed of!—This organization was strong enough to withstand bad emperors: the accident of personality has nothing to do with such things—the first principle of all genuinely great architecture. But it was not strong enough to stand up against the corruptest of all forms of corruption—against Christians… These stealthy worms, which under the cover of night, mist and duplicity, crept upon every individual, sucking him dry of all earnest interest in real things, of all instinct for reality—this cowardly, effeminate and sugar-coated gang gradually alienated all "souls", step by step, from that colossal edifice, turning against it all the meritorious, manly and noble natures that had found in the cause of Rome their own cause, their own serious purpose, their own pride.

The sneakishness of hypocrisy, the secrecy of the conventicle, concepts as black as hell, such as the sacrifice of the innocent, the unio mystica in the drinking of blood, above all, the slowly rekindled fire of revenge, of Chandala revenge—all that sort of thing became master of Rome: the same kind of religion which, in a pre-existent form, Epicurus had combatted. One has but to read Lucretius to know what Epicurus made war upon—not paganism, but "Christianity", which is to say, the corruption of souls by means of the concepts of guilt, punishment and immortality.—He combatted the subterranean cults, the whole of latent Christianity—to deny immortality was already a form of genuine salvation.—Epicurus had triumphed, and every respectable intellect in Rome was Epicurean—when Paul appeared… Paul, the Chandala hatred of Rome, of "the world", in the flesh and inspired by genius—the Jew, the eternal Jew par excellence… What he saw was how, with the aid of the small sectarian Christian movement that stood apart from Judaism, a "world conflagration" might be kindled; how, with the symbol of "God on the cross", all secret seditions, all the fruits of anarchistic intrigues in the empire, might be amalgamated into one immense power. "Salvation is of the Jews."—Christianity is the formula for exceeding and summing up the subterranean cults of all varieties, that of Osiris, that of the GreatMother, that of Mithras, for instance: in his discernment of this fact the genius of Paul showed itself. His instinct was here so sure that, with reckless violence to the truth, he put the ideas which lent fascination to every sort of Chandala religion into the mouth of the "Saviour" as his own inventions, and not only into the mouth—he made out of him something that even a priest of Mithras could understand… This was his revelation at Damascus: he grasped the fact that he needed the belief in immortality in order to rob "the world" of its value, that the concept of "hell" would master Rome—that the notion of a "beyond" is the death of life. Nihilist and Christian: they rhyme in German, and they do more than rhyme.