I had Britain in mind when asking this and the competition between Irish and Roman schools of Christianity, but I've heard mention, with no sources, of Gallic, Burgundian, and Egyptian schools as well. How many schools were there, and what were the differences between them?
May I ask precisely what you mean by schools? Schools of thought? Liturgical Rite (Gallic, Salic, Ambrosian, Mozarabic, Alexandrian, Byzantine)? Or something else?