Other answers address the big user experience advantages (e.g. threading) that it has over Slack, but there's a bunch of smaller features we have that I don't think Slack does (e.g. you can configure regular expressions to automatically linkify patterns like T123 to link to your bug/ticket tracker).
In terms of features Slack has that Zulip doesn't, I think the biggest ones are features that Zulip has today on zulip.com (which isn't taking new users) but you can't easily setup for your own Zulip server (e.g. the Android app doesn't support talking to a custom server without patching it yourself, mobile push notifications aren't available with your own server, etc.). Contributions on those things are welcome -- they're all relatively easy problems for someone with some mobile experience.
In terms of features that aren't just missing configuration in the run-your-own-server model, I'd say the biggest one is that Slack has a really slick onboarding experience and it has more slick integrations. It's hard to compete on onboarding with a company with like a hundred engineers, but I don't see the integrations piece as being a long-term advantage for Slack -- they're easy to write and I expect the open source community to produce a lot of them for Zulip over time.
In terms of features Slack has that Zulip doesn't, I think the biggest ones are features that Zulip has today on zulip.com (which isn't taking new users) but you can't easily setup for your own Zulip server (e.g. the Android app doesn't support talking to a custom server without patching it yourself, mobile push notifications aren't available with your own server, etc.). Contributions on those things are welcome -- they're all relatively easy problems for someone with some mobile experience.
In terms of features that aren't just missing configuration in the run-your-own-server model, I'd say the biggest one is that Slack has a really slick onboarding experience and it has more slick integrations. It's hard to compete on onboarding with a company with like a hundred engineers, but I don't see the integrations piece as being a long-term advantage for Slack -- they're easy to write and I expect the open source community to produce a lot of them for Zulip over time.