Ask HN: Claude Pro vs. Claude via Kagi Ultimate

A subscription to Claude Pro gives access to Extended Thinking and the web (via Brave). A subscription to Kagi Ultimate gives Claude with Extended Thinking, as well as many other LLM models, access to the Kagi search engine.

On one hand, giving Claude access to Kagi should be superior to Brave. However, I don't know if the quality of Claude in Kagi is truly equivalent to Claude via a subscription through Anthropic.

Has anyone done a serious comparison of the two?

Thanks!