Media discourses affect people’s attitudes towards refugees and migrants, and from there even migration and asylum policies. Earlier research shows that traditional and social media accommodate different discourses and encourage different attitudes to migration and asylum. On the other hand, traditional media adapted to technological developments and the growth of digital communication platforms by introducing digital components. We study whether such hybridization led to convergence between the social and traditional media types during the European migration crisis. Using a mix of computational and qualitative methods on 20 million media items from nine European languages across both media types, we identify the main cleavages and topics described within the different subsets of media. Summarized, our results show that discourses are remarkably similar across languages. In contrast, there are clear differences between social and traditional media. On the one hand, traditional media had a more fact-based focus on the description of individual events linked to the European migration crisis and the national dimension of the crisis and national actors. On the other hand, social media focused much more on the expression of opinions, and on the European dimension of the crisis, as well as on EU actors. Despite trends towards hybridization, we thus find that traditional and social media discourses on migration and asylum retain their distinct characteristics.