The growth of diet-related diseases is becoming an important societal concern and a challenge for a more sustainable society. This has developed important trends in food consumption, including the increasing demand for food with a natural attribute and with health claims (e.g., enriched food). Consumers tend to evaluate these two attributes as superior ones and tend to pay a premium price for them. Accordingly, the value added by producers also will upturn if they take into consideration the consumers’ preferences. However, to the best of our knowledge, consumer preference over the two types of products (natural and enriched) is not yet completely clear. The present study tries to contribute to reducing this gap by analyzing Hungarian consumer preferences for natural fruit juices over enriched ones and exploring the drivers which guide consumer choices for the two attributes. For this purpose, we analyze young consumers’ willingness-to-pay (WTP) for natural and enriched fruit juices using a seemingly unrelated regression (SUR) to derive the two value-added activities. Our results show that the fruit juice with the natural attribute is preferred over the enriched one, and that there is a common feature behind the perception of the two attributes, namely the healthiness. Based on the natural fruit juice characteristic, these results open space for local production in gardens or in small-medium sized farms. This could have beneficial effects, both for sustainable development of rural areas and for the promotion of healthy food systems towards sustainability in food consumption.