The verdict
If you are a support team of a few agents to a few dozen and want a mainstream tool at a sensible cost, I'd start with Freshdesk. If you need deep structure, workforce management, many channels and a large ecosystem, or you expect to grow into an enterprise team, pick Zendesk.
In both, the plan price is not the full cost. Ask for a quote with your expected agents and AI volume, and check which tier holds the AI agent and the channels you need. Plan a few weeks of setup either way. Test the AI on your own tickets before you depend on it.