The verdict
For a small team that wants AI to take a share of routine questions from day one, I would look at Intercom first. Start with one channel and measure resolved conversations before widening.
If support is a real function with several agents, and you need routing, triggers, reporting and a large app marketplace, pick Zendesk. Plan time for an admin to set it up properly.
If you are a small team with simple email needs and a tight budget, I would skip both and compare Freshdesk or Help Scout. Both of these tools get expensive once you add the AI and channel features you actually want.