Tavily, Brave and Exa get compared on relevance, but the structural thing to know is what they return: ranked results with snippets — a few hundred characters each — not pages. An agent that "searches the web" with only a search API is reasoning over fragments.
The architecture that works is two-stage: search to find candidates, then a fetch/extract step (the agent's own HTTP + readability, or a scraping API) to pull full content from the top hits. Skipping stage two is the root cause of a whole genre of agent failure — confident answers assembled from snippet shards that misrepresent the page.
The APIs differ in how much they help with stage two: some offer content extraction on request, at extra credit cost; raw-search tiers leave it entirely to you. Compare them on that, not just on ranking quality.
Free quotas and the extraction options, side by side: https://toolfreebie.com/tavily-vs-brave-vs-exa-search/
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