Which type of potato is healthiest? Among the commonly available varieties, it would be the sweet potato. In the raw form it has an ORAC value of 902 and after it is baked, it's 2,115.
Given its bright orange color, this is not surprising. There is a high correlation between the color intensity of fruits and vegetables and how much antioxidants they have. That's why the orange is healthier than the white. It isn't a hard and steadfast rule, but it's more often the case than not.
Among all - both common and special varieties - which sweet potato is healthiest? That award would go to the purple yams (technically they're not yams, yet most people call them that). Their rich color contains a high amount of anthocyanins; peonidin and cyanidin. By far it has the highest amount of antioxidants and keep in mind, this ORAC represents the fresh, raw potato. Upon cooking, it is likely that value would go up. That's not because the amount increases, actually quite the opposite - the heat of cooking degrades some antioxidant content. The reason the value increases for cooked potatoes is because they shrink, and therefore, they are more dense on an equal weight basis (i.e. 100 grams of cooked purple sweet potatoes vs. 100 grams raw).
Research Support, Non-U.S. Gov't: Antioxidant activities, phenolic and b-carotene contents of sweet potato genotypes with varying flesh colours. Food Chemistry Volume 103. Pages 829-838. USDA 2007