Is purple cauliflower more nutritious and healthier than white? A one cup serving contains around 400 mg of anthocyanins - those are part of the dark purple pigment and they are a potent antioxidant. Compare that to the white, which has virtually none. But whether you eat the purple vs. white cauliflower, the good news is that both contain high amounts of glucoraphanin, which is a phytonutrient that is unique to the family of plants they come from (cruciferous). Glucoraphanin, which is part of a category compound known as glucosinolates, has been studied for numerous possible health benefits, including research which suggests it might have anti-cancer properties, at least in vitro (in test tubes).
To put the purple cauliflower's antioxidant content in perspective to white, it's about 2.5x higher.
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