The verdict
If you run a Shopify or similar store and support takes real hours every week, pick Gorgias. It does one job and does not make you pay in complexity for features a store never uses. If you are a software or services business, or you need phone, workforce management and a large ecosystem, pick Zendesk.
Watch how each is billed. Gorgias is priced by ticket volume, so a seasonal spike can push you up a plan. Zendesk is priced per agent, with several capabilities sold as add-ons, so ask for a full quote. Either way, the AI agent needs supervision at first.