Organic food and drink is undoubtedly a growing market. Consumers perceive organic food as healthy, and nutrition claims (NCs) and fortification may add to this perception. Whether this is true is still a matter of controversy, particularly for organic food products. We present here the first comprehensive study of large samples of six specific organic food types, analysing the nutritional quality (nutrient composition and “healthiness”) as well as the use of NCs and fortification. In parallel, a comparison with conventional food is also carried out. For this purpose, the Food Database of products in the Spanish market, BADALI, was used. Four cereal-based and two dairy-substitute food types were analysed. Our results show that as many as 81% of organic foods are considered “less healthy” by the Pan American Health Organization Nutrient Profile Model (PAHO-NPM). Organic foods present a slightly improved nutrient profile compared to conventional foods. However, many of the differences, though statistically significant, are nutritionally irrelevant. Organic foods use NCs very frequently, more than conventional foods, with very little micronutrient fortification. The main conclusion of this work is that consumers’ perception that organic food products are healthy is unfounded from a nutritional point of view.