This controversy that Blessed Duns participated in is only the tip of the iceberg. The Dominicans and Franciscans are contemporaries, both founded in the early 13th Century, and the Jesuits, though they came around 300 years later, joined in a very vigorous, sometimes brotherly, rivalry among the three.
The three orders often had debates regarding the doctrine of the Immaculate Conception, which was not defined as dogma until the 19th Century, and which is basically rejected by the Eastern Churches, unless you can reformulate it carefully in Greek.
They also had debates about missionary activity and the "Chinese Rites Controversy" was a huge factor in how East Asia would be evangelized, and how they would worship, and whether indigeneous peoples worldwide are able to contribute their faith practices to Roman Catholic liturgies at this late stage of development.
There's an old joke they have, which goes: "The Dominicans were founded to combat the Gnostic heresy of the Albigensians. The Jesuits were founded to combat the heresy of Protestantism. Who was more successful? Have you met any Albigensians lately?"