In search of differences and similarities in relation to the role and location of science in European societies, we use empirical information from 37 countries as a platform for developing typologies concerning dimensions of science in society. These capture clusters of countries and reveal significant heterogeneity across Europe, providing a point of departure for international learning, while also demonstrating the challenges that the European institutions face in their promotion of a European Research Area, shared priorities and a common model of science in society. Combining national-level and individual-level data, we further show a connection between national differences and the public's satisfaction with their own role as participants in science and technology. In countries where science communication culture is weak, where science plays a minor role in policy-making, and where institutions and procedures for public involvement are weak, citizens are comparatively less contented with their own involvement in science and technology.