If they each give the correct answer in the same number of steps then there’s no reason to prefer one over the other.
That being said, I had been using web search for several years looking for the Get Smart episode I had seen as a kid in the 1980s where the enemy agent explains that he can't give up his suicide ring because "That's how it works, if I take it off, my wife will kill me." Google Bard found the episode on the first try.
So, I tend to fall back to LLMs only when search engines fail me.