To what extent political parties engage in debates about the same issues and how they respond to each other is highly relevant to democratic processes. Existing research on issue engagement has uncovered several interesting patterns and factors, but has neglected one important feature of contemporary democracies: nowadays, political actors have a wide range of communication channels at their disposal with the use of ‘newer’ forms of political communication (e.g., social media) potentially transforming discursive power relations between political actors. However, it remains largely unclear whether the extent and nature of issue engagement varies between more ‘traditional’ and ‘newer’ forms of political communication. To fill this gap, I apply unsupervised topic modelling to press releases and tweets from political parties in Austria, Germany and Switzerland (January 2019–September 2021). The statistical analysis shows substantial differences in issue engagement between political parties in press releases and on Twitter, now X. First, I find a higher likelihood of issue engagement between parties in tweets. Second, Twitter appears to moderate the influence of party‐level factors on issue engagement compared to press releases. The results show that for issue engagement in tweets, the importance of party size is smaller and the role of government parties is larger than in press releases, while the role of ideological distance does not seem to change. These findings add important insights to our understanding of the potential transformative effect of new communication technologies on party competition and political discourse.