You may be shocked to hear that the boiled version of red or purple cabbage has a higher ORAC value than the raw version. But don't be surprised because there's a good reason for that. When food is boiled, it reduces the amount left (that's why clamshell of fresh spinach cooks to become almost nothing). The reason the boiled version is higher is because more water is removed during the cooking process, leaving a higher concentration of fiber and nutrients (relative to fresh) in what goes on your plate.
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