It's hard to imagine today's equivalent to the 17th-century French academy's battle between the poussinistes and rubenistes, between design / line and color, between Andre Felibien and Roger de Piles. At the heart of this battle were theories about the "unity of action in painting." Also important was the fundamental problem of painting's depiction of subject matter and the visual effectiveness of depictions—a rational or literary priority versus a priority on strictly visual effects.
Today we'd have trouble defining what "painting" or its sui generis is. The Cubists and Dadaists eroded the stability of such definitions more than one hundred years ago. Today's painter finds her way, with or without an attendant theory, and hopes enough people see it her way to make her efforts plausible.