The biggest difference I see is that Discord is "free" for communities, or at least the model is different: an individual user can apparently pay to contribute to the server and "unlock" features. Also I think Discord just comes with history for free, which is a killer feature in many communities.
Slack is more "meant for companies" in the sense that the "owner" of the server (i.e. the company) has to pay each month for each user. Many open source communities can't afford that, which is why they like the Discord model better.
Disclaimer: I hate both, because they don't have an open API and the Desktop apps use ElectronJS. So I'm not sure if I'm biased towards one or the other :D