I'm not sure that Christianity (whether Orthodox or not) was that popular, even in the Eastern Empire; it constituted probably about a tenth of the Roman population, not nearly a third, at the time of the Milvian Bridge.
As for the First Ecumenical Council, it excommunicated just the Arians; Nestorius was not on the scene yet, and Monophysitism (that Jesus had only a divine nature) was an equal and opposite reaction
against Nestorianism (that Mary did not bear God,) not a derivative, a position not resolved until the Fourth Ecumenical Council at Chalcedon. Despite the First Ecumenical Council's rulings, the Emperors continued to support Arian bishops and teachings until Theodosius came on the scene some fifty years later, when he made Orthodox Christianity the sole state religion.
The main threats to the Roman Empire in the XI century AUC (4th century AD) were the Germans (being driven by the Slavs and Huns into the Roman Imperium) in the West and the Sassanid Persians in the East. Depending on how Rome resolves its own Civil War among competing Emperors, we will see either a quicker German takeover of the West or a faster Persian conquest of much of the East.
Now for the ongoing War of the Tetrarchy: With Maxentius the usurper victorious at the Milvian Bridge, he would likely send a force to the East to overthrow Licinius, the legitimate Augustus, in favor of Maximinus. (In OTL, Licinius defeated Maximinus at Tzirallum in Asia Minor a year after the Milvian Bridge despite being outnumbered seven to three. Would Licinius be able to defeat Maxentius and Maximinus together? It's practically a coin toss, but I would give the victory to Licinius.)
With Licinius' victory in the East, he has two options: 1) destroy the usurper of Rome and unite the Empire, or 2) abandon the West and concentrate on defending the East against the Persians. Option 2, I think, is more likely. The Empire is now split permanently, and Licinius has in effect abandoned the West to the Germans. This said, where will Licinius make his new capital? Athens? Thessalonica? Nicomedia? Troy? Antioch? Alexandria? Or somewhere else, like...
Byzantium!