I've been unable to find the source for the quote but there's a statement made by someone in the 18th or 19th century about how the civilisational clash is between Rome and Geneva. The point being, the Geneva in question is not the Geneva of Calvin but of Rousseau and Voltaire. In other words Geneva represents not the Reformation but the Enlightenment.
Obviously this statement (as striking as it might be) is somewhat flawed. The situation is really much more complicated and Rome is by no means exempt from Enlightenment influence. Additionally, you won't find many philosophers or historians that will agree on when the Enlightenment started or ended and whether a good deal of 19th and 20th century philosophy qualifies as an outworking of the Enlightenment or a response to it.
This is not to say that all responses to it are positive or do anything to remedy the crisis and the culture the Enlightenment spawned.
While trying and yet failing to hunt down the source of the quote I stumbled on a book and subsequent articles concerning a revisionist work on Enlightenment Geneva. Jennifer McNutt, (the author and a professor at Wheaton) is a theological liberal and is ordained in the PCUSA. To her way of thinking the Enlightenment culture of 18th century Geneva was not only something to celebrate but a natural outgrowth of Reformed theology and scholasticism. I could not help but smile - her thesis is certainly wrong but with more than a hint of historical truth.
Unbiblical in every way, there is nevertheless some truth to the assertion. History has repeatedly demonstrated that philosophical theology and scholasticism create a progressive dynamic that is not easily arrested. Ultimately it becomes self-destructive. The confessions of the Magisterial Protestants attempt to arrest this process but they too are fraught with problems and inconsistencies and so like it or not, the progression continues. Confessional-ism only works when attached to a robust polity. If this is absent or if the polity is controlled by the state - that has other interests apart from orthodoxy, the confessional anchor will certainly come loose. The McNutt work (Calvin Meets Voltaire: The Clergy of Geneva in the Age of Enlightenment, 1685–1798) is not something I'm likely to spend money on though I am somewhat curious to determine how she makes her case. The value is found in that it exposes an ugly truth regarding aspects of the theological heritage that the Confessionalists don't want to acknowledge.
So for McNutt and the theological liberals (that are mostly unbelievers), there's no conflict at all. For others the Rome vs. Geneva conflict is existential - the battle between Christendom and the Secular Humanist culture of Modernity.
But ultimately as Christians we should understand this is a false conflict, a false dilemma. The war is real to a point but in another sense it's farcical. What we're witnessing is not a monumental epic clash for civilisation and the future history of the world. On the contrary it's something much more basic. It's a civil war, a Babylonian Civil War.
In terms of the book of Revelation it's a case of clashing hydra-heads, one devouring the other. And as soon as one dies, another will arise. The imagery is also found in Daniel - the beasts fight against each other and destroy one another, but in Revelation they're revealed as one composite Beast.
There is an epic eschatological conflict of which we are a part but it's not Rome and Geneva who are the combatants. Rather it's a case of Zion vs. Pseudo-Zion. It's the battle of Har-Maggedon - not a contest for temporal civilisation but for the very Throne of Heaven, the position of authority in presiding over the Divine Council.
Another way of expressing the battle is to understand Pseudo-Zion as Babel - the counterfeit mountain, the Pseudo-Zion. As such both Rome and Geneva are part of the whole Babel-Babylon-Shinar complex of the world and its false religion which includes the False Church. The civilisation built by Rome in the aftermath of Constantine and Theodosius is not Zion but rather is Babel topped by a cross, the Bride turned Whore riding on the Beast.
As I've written before this line of thought always takes me back to my trips to Rome and the many obelisks found there. The symbolism is largely the same as that of Babel - the divine axis, the mountain of God, the nexus between Earth and heaven. In every case these stylized mountains are topped with crosses placed by the Roman Catholic Church. It's quite a statement and in fact says a great deal more than Rome actually realizes.
Today, in American culture the symbolism is more mundane but also found when you drive by a steepled church building flying the flag of the Beast-empire out front. American Evangelicalism is this culture's version of Roman Catholicism and every bit as corrupt and lost. And so while it's in a desperate fight to maintain its Babel and is under threat from a rival one - for the Church of the New Testament, it's just a case of clashing Beasts.