Let us assume that the Germanic tribes, especially the Goths, were converted to Nicene Christianity rather than Arian Christianity. Perhaps Ulfilas himself is Nicene. Or another missionary converts them. Doesn't really matter.
How does this alter the tribes' interactions with the Empire? Consider that, during a large chunk of the middle of the 4th century, the leadership of the Empire was all over the place, religiously. There were Nicene Emperors, Arian Emperors, and, of course, one Apostate Emperor. Hell, Valens was Arian while ruling the East, and his brother, Valentinian, was Nicene, while ruling the west. For sake of ease, let's assume that the Romans resolve their own issues with Arianism pretty much the same as historically, tending towards Nicene.
Presuming that there's no real changes to the fall of the west, how might the Roman populations interact with Germanic leaders that don't have a religious difference?