Pros: Server maintenance is blissfully minimal. Message threading that actually works. No server issues or downtime in the past 4 years. (Every time I see a HN "Slack is down" posting, I smile to myself and continue my work day...) It runs great for ~50 employees on an AWS t3a.large instance. Importing all the company's previous messages from Slack worked perfectly.
Cons: If you have people used to Slack, there will be resistance / a learning curve. Knowing, "when do I create a topic?" takes practice. The mobile and desktop apps are not as polished as Slack's. Not as many integrations as Slack. You have to know enough to manage and secure a server yourself.
The Zulip devs accept Github donations, btw, if anyone cares to support their work. (We do; no affiliation other than we're happy to have a private, self-hosted alternative.)
edits: punctuation and adding that instance was a ".large"