I was asked to weigh in on this question recently. Here’s my answer: it depends on what you mean by Babylon the Great, and of course, what you mean by “destruction”.
By “Babylon the Great” I don’t mean the ancient empire of Babylon under any of its ancient dynasties. I mean the symbolic Babylon the Great described in the biblical book of Revelation: the Roman Catholic Church. She is described in Revelation 17 as a Prostitute–a false bride, impersonating the true Bride of Christ, the Church. Babylon the Great pretends to be a church but is unfaithful to Jesus Christ. But the Bible prophesies that the Roman Catholic Church, from its once great height of worldly power with armies at her command, would fall in stages before her final, terrible end at the second coming of Jesus Christ. (This is a really good reason to get serious about praying for people you know who are Catholics, and sharing the Gospel with them. Jesus says, in Revelation 18:4-5, “Come out of her, my people, lest you take part in her sins, lest you share in her plagues; for her sins are heaped high as heaven, and God has remembered her iniquities.”
Revelation 17-18, as Oral Collins rightly argues, enlarge and zoom in on what had been predicted to occur under the bowl judgements of Revelation 16. The Roman Catholic Church is now seen humiliated. No longer having the status she had while the Popes ruled as one of the heads of the beast, she is now sitting on the beast, along for the ride, and under the rule of the 10 nations of Roman Europe. And 17:16 says they hate her. The judgement that began with the fourth and fifth bowls, so since the French Revolution, portray the progressive humiliation of the Roman Catholic Church, the international reach of the Catholic Church into many nations (she “sits on many waters”), but the corresponding international scandal as her corruption becomes widely known. Chapter 18 graphically describes the status of the Roman Catholic Church today, and since 1870, with no more temporal power, but still dressing like and pretending to be a queen. It’s important I think to notice that her final death is not actually described prior to the second coming of Christ. In Rev 19:2 her judgement is pronounced; in 19:20 the clergy of the Roman Catholic Church is destroyed along with the beast. This parallels 2 Thess 2:8 which predicts that the Antichrist (the popes) will finally be annihilated by the actual appearance of Christ’s coming. The seventh bowl (Rev 16:17ff) seems to predict massive destruction on Roman Europe, even splitting into three parts. While the bloodbath of the First and Second World Wars certainly goes a long way to fulfilling the violence and ruin predicted to fall upon the peoples and nations who commit adultery with the Roman Catholic Church–and obviously upon Rome herself–I think there remains to be seen a fulfillment of the breakup of Europe into three parts. The way the seventh bowl and the events of chapter 19 seem to be closely connected suggests in my mind, parallel with Mark 13:24-25 and Jesus’ prediction of the fall of Roman Europe (if that explanation of Mark 13 surprises you, check out my sermon on that passage here). So we should expect to see a kind of destruction of Europe that reduces its government and civilization to chaos, shortly before the return of Jesus.