As is the case with many vegetables, the skins are one of their most concentrated sources of nutrients. This is one reason why processed baby carrots contain less antioxidants than the whole carrot, an amount about 37% lower. But since the vast majority of people peel their carrots anyway, it's not really a fair comparison.
ORAC Source
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