I think Christianity might come out on top in places like Central Asia, Arabia, and especially Africa.
No Islam tearing Rome to shreds leads to at least a decent political reconsolidation, and if even if they halted any expansion and remained in the territories prior to the Islamic invasions, they'd still be a super wealthy state. Assuming there's still a Trans-Saharan Trade (which there should definitely be), the Christians fill the gap of the Muslims and trade with the West African Kingdoms, which would lead to the same sorts of conversion that the Muslims undertook OTL. Plus the Axumites would be a major trading force across East Africa, and like Islam before, would probably spread Christianity through trade.
Plus Persia in itself had already been swinging towards Christianity, the vast majority of Mesopotamia was Christian, and multiple consecutive Emperors like Kavadh II, Ardashir III, and Shahrbaraz were all extremely friendly to Christianity. Nestorianism had already spread even as far as Central Asia, and with no Islam to knock it down, and a pro-Christian Iran, it could largely come to dominate the region. Arabia as well was dominated by the Christian Lakhmids and Ghassanids, and the religion would definitely seep far in, but might be counteracted by the extremely large Jewish populations.