Differences among Christian writers on the war question goes back to the pre-Constantine period. For example, some Church Fathers weighed in on different sides of the question of whether Christians should be soldiers.
Just-war theory receives its first full statement (that I know of) with St. Augustine of Hippo, writing about 100 years after Constantine. So there’s not really a body of primitive doctrine on the question. This makes sense, because Christian writers wouldn’t have had much incentive to make policy recommendations to rulers while they were a persecuted minority.
One of the obvious ways in which the Church changed post-Constantine was in developing a more formal structure modeled on Roman administrative jurisdictions (the diocese). Bishops had been around from early on, but the “institutionalization” of the Church certainly ramps up in the fourth and later centuries.