Organic production is gaining an increasing share of the vegetable market since it is promoted and perceived by consumers as healthier and safer for the environment. Despite the general acceptance of these benefits, the alleged higher nutritional value of organic compared to conventional products has not been well defined in terms of physiological processes. The lower yield observed under organic farming is likely caused by genetic determinants of specific varieties used in this system and/or an exposure to biotic and abiotic stresses that may affect organic crops. In response to these stresses, plants physiologically accumulate organic molecules that in addition to have a protective function for the plants may also have potential health benefits (antioxidants). In this general frame, this review discusses the concept of physiological quality, defined as the commercial (e.g., sugar content, fruit firmness, % dry matter) and nutritional characteristics (e.g., concentration of vitamins, antioxidants, minerals and other valuable health-related molecules) of the harvested product determined by physiological responses to a specific cultivation process/regime. Main biotic and abiotic stresses occurring in vegetable crop systems, with an emphasis on key differences between organic vs. conventional farming, are described. Functional links between accumulation of nutritionally valuable molecules, organic farming, environmental and cultural stresses are then discussed. Finally, how plant breeding may contribute to improve organic crops is briefly addressed. We overall highlight that organic farming may have intrinsic values associated to the peculiarities of the cultivation process per se that so far have not been sufficiently considered and exploited.