the outer surface of a ring (circle) if made of solid material, will resist flex better than the flat sides or the outer surface of a triangular shape.

however, for the purposes of a rifle barrel avoiding flexing or oscillating, a circular tube will flex more easily in the middle of its shaft than a triangular one.

in other words, if you extended the circular and triangular barrels to 10 feet long, but otherwise kept them the same weight and material, the circular one would sag in the middle more than the triangular one, at any point of rotation.