Does red cabbage have antioxidants? Yes, the purple pigments in it are a rich source of anthocyanins, which are responsible for much of the total antioxidant content in the vegetable. The boiled version maintains a high amount. Purple cabbage and red cabbage are the same thing, it's just a preference as to what you prefer to call it.
USDA Database for the Oxygen Radical Absorbance Capacity (ORAC) of Selected Foods, Release 2 - Prepared by Nutrient Data Laboratory, Beltsville Human Nutrition Research Center (BHNRC), Agricultural Research Service (ARS), U.S. Department of Agriculture (USDA) - May 2010