The aim of this paper is to understand public preferences for several future scenarios of achieving a healthier, more equitable and sustainable Europe, which differ in the way the society is organized (individualistically vs. collectively) and in the driving sector (public vs. private). To achieve this aim, we conducted a questionnaire survey using representative samples for five European countries in 2018. About three thousand respondents chose among the four scenarios presented within four different contexts (green spaces, active mobility, energy-efficient housing, food consumption) or none of them. A majority of people in the five European countries were ready to accept one of the scenarios. We found significant differences in preferences according to socioeconomic backgrounds and values of respondents. People above 35 years old, those who were less educated, and those in the lowest household income tertile were less supportive of all scenarios. The heterogeneity in preferences associated with differences in socioeconomic backgrounds was larger for the scenario in which society is organized individualistically and driven by the private sector. Smaller distinctions were found in case of the scenario in which society is organized collectively and is driven by the public sector. Departing from social psychological theories, we examine the role of altruistic, biospheric, egoistic, hedonic, and security values. People with stronger biospheric values were more likely to accept scenarios, particularly those which are driven by the public sector and where there is more collective organisation. Those with a more egoistic value orientation were more likely to have higher preferences for scenarios where the private sector had a dominant role. The policy implications, in terms of the selection and framing of policy measures to enhance public support, are discussed.