Using the 2016 Brexit campaign as a case study, the proposed paper compares how the Leave and Remain positions were discussed on Facebook and Twitter. We argue that these platforms’ potential for acting as deliberative arenas varies depending on their digital architectures (i.e. their feed algorithms, the ‘Friend’ or ‘Follower’ relationship, and the degree of visibility of their posts). We test this argument by comparing, over the entire duration of the campaign, citizens’ comments made to the public Facebook pages of the Leave and Remain campaigns, as well as citizens’ Twitter messages using the corresponding hashtags on Twitter. Using supervised machine learning methods in R, we identify discursive frames indicating homophily among users (e.g. agreement) or heterogeneity (e.g. disagreement). We expect to find that Facebook is more likely to host discussions among like-minded users (homophily), whereas Twitter debates are more likely to be more confrontational, taking place between users holding opposing views (heterogeneity). The results are discussed in light of social media’s democratic potential.