It really depends on what you ask for, how you ask and which bot(not) you are using. Without these any comparison will be incomplete.
For instance, I heavily use perplexity and it completely changed my search behaviours. Especially, if I am looking on information from Reddit, I select focus mode and it generally provides good answers than search engine.
LLMs enable you add context or examples, so they can find relevant information. With all caveats, most LLMs are better than search engines on privacy questions, especially without internet scanning. Because it eliminates the seo garbage.
I use different LLMs for different purposes such as ChatGPT 4 for work, perplexity for internet search and huggingface without an account for sensitive questions. You can use perplexity without an account but I have one because at the end of the day, I have very few sensitive data or questions there.