Zapier wins the first afternoon. If the job is "when a form is filled, add a row and send a Slack message", a zap does it today with no code and no builder. Its limits show up exactly where small business work gets valuable: the steps that need reading, judgment, and drafting. A zap can move an invoice; it cannot decide whether the invoice looks wrong.
Claude Code is the opposite shape. There is a real setup hump, and the honest path for a non-technical owner is having someone build the first pipelines with you. But what you get is automation with judgment in it: read the inbox, extract the figures, flag the anomalies, draft the reply, and log what happened. The output is plain scripts you own, not workflows rented from a platform, and the flat plan pricing does not climb with every task the way per-task billing does.
The practical answer for most owner-operators is sequencing, not either-or. Keep Zapier for the shallow app-to-app handoffs it is genuinely good at, and move the deep recurring work, reporting, document handling, client correspondence, onto agent-built pipelines as they prove out. When more of your week runs through the second category, that is the signal to make the agent lane your operating layer.