The Christian God won out over those of ancient Rome for many reasons, but most basically because there were significant numbers of people in the Empire who were "frustrated" in Eric Hoffer's definition in The True Believer (1951): "people who, for one reason or another, feel that their lives are spoiled or wasted" — and who felt that their lives could be improved in the Christian Church. Primarily this was because the primitive Church offered community: it continued the Jewish synagog system but improved on it by making Christian congregations more open and "proactive," recruiting actively among the gentiles and soon freeing male gentiles from circumcision and all Christians from Jewish dietary laws and other segregating inconveniences. The Church also offered hope. If it outdid the Jews at offering a structured and protective community, it competed effectively with the Mystery Cults in offering comforting expectations of immortality and a New World Order far better than anything offered by any increasingly corrupt and parasitical Imperial bureaucracy. In a crumbling world — with old oppressions hanging on while much else changed all too fast — the Church offered "Faith, Hope, and Love," and equal to these, immediate community and at least local stability.
Rome in the West fell to the Germanic tribes not because of some sort of Prussian military prowess in a massive German invasion, but because the Empire was weakened greatly by refugees from the Huns and because (along with other reasons) there were many people in the Western Empire who had no strong inclinations to shore up that increasingly corrupt, distant, and ineffective Imperial rule. Between the Imperial status quo and opportunities among the newcomers, significant numbers joined the barbarians.
Much of the Roman Empire in the East — pretty much all but the rump state of the Byzantine Empire around Constantinople — fell to the forces of Islam, finally bringing to an end the Ancient World. The dominoes fell not because the Muslim fighters were all that numerous or fanatical, although many were jihadist True Believers, but because large numbers of the peoples in the fading Ancient World had little stake in the Eastern status quo or the tribal system in North Africa; and many middle-class and common folk had much to gain if they went with the flow and submitted to God as Allah, and the power in this world of religio-political Islam. Taxes would be no higher; the new governments were at least honest and energetic, and soon enough the rules were clear with the development of Sharia law; and the new faith was democratically straightforward and hopeful. As Christianity had done earlier, but in a more concentrated way, Islam gave people hope, and gave many people's lives structure and purpose.
Within a few hundred years, from 623 to the 1050s and beyond, Islam also offered victory and conquest and for Muslims thereafter a glorious history to look back on.
Nowadays we have The Islamic State of Iraq and Syria (ISIS) and/or the Islamic State (IS) and/or the Islamic State of Iraq and the Levant (ISIL) and/or, with some redundancy in English, the State of the Islamic Caliphate (SIC).
The Caliphate has been taken seriously lately by The Powers that Currently Be, and should be.
The numbers of ISIS's combatants may be small, but small numbers can undermine whole societies if introduced into larger populations ready to at least acquiesce in radical changes. The holy warriors of the SIC, moreover, are fanatics and constitute a potential core of a mass movement that can inspire other movements in alliance with them or in violent opposition to them. The men of ISIS have helped create a realm of refugees and move in large areas of displaced people: people physically displaced by warfare, others more comfortable, but psychologically displaced in a modern world that seems militantly secular and committed to constant mutability: a threatening new world where "All fixed, fast frozen relations, with their train of ancient and venerable prejudices and opinions, are swept away, all new-formed ones become antiquated before they can ossify. All that is solid melts into air, all that is holy is profaned ... ."
Rome as "the Eternal City" decayed, was sacked, and decayed again for an age; Rome as an empire fell three times — three counting the conquest of Constantinople by the Turks in 1453; and if one seeks successors to Rome, Moscow has a claim, and the Chinese have an argument. From the 1st century A.H. (anno hegirae, After the Hegira) to Early Modern times, however (say 622 C.E. to 1492) — for a large hunk of human history, the best contender for the successor to Rome was a House of Islam that extended through much of the territory from Spain through Indonesia.
If the current claimants to the Caliphate can find themselves a Leader with the charisma and skill of a Mohammed or Saladin, combined with the fanaticism of a suicide bomber, we can be in for a period of jihads and crusades that will remake our world, and destroy, minimally, much of our world.