From my experience the Google AI mode is more restrictive on what it will let you search for and the content it produces.

I personally have had to use DuckDuckGo to search for things that Gemini finds to be against its instructions to answer.

And I'm not talking about things that are NSFW, but some things that Gemini just doesn't want to discuss.

That's kinda Gemini's problem in general, it just is overly restrictive and doesn't like to talk about anything things that Claude will freely talk about and push against and discuss with you.