The USDA did not provide testing results for cooked spinach to compare it versus fresh spinach. Though they did test frozen, which actually ranks higher than fresh. In terms of whether cooked spinach is as healthy as fresh - for antioxidants and vitamins - that really depends on the method used to prepare it. Inevitably some nutrients will be lost, but there is a big difference between flash steaming the leaves versus immersing them in boiling water for several minutes. As a general rule of thumb, the healthiest way to cook spinach - regardless of method - is to cook for the minimal amount of time necessary to achieve the texture and taste you desire. Steaming is best, since less of the vitamins and minerals are washed off (when compared to boiling water, in which you drain).
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