Private search engines: what switching actually changes
What 'private' actually means here
A private search engine's core promise is that it does not build a lasting profile of you from your queries: no search history tied to an account, no personalized ad targeting based on what you looked up last week. That is a real, meaningful difference from the default, even though the site you eventually click still sees you arrive.
It is worth separating two things people lump together: privacy (who stores your searches) and independence (whose index the results come from). Some private engines run their own crawler; many privately re-serve results from a large provider. Both can be private; only the former is truly independent.
Choosing by what you actually want
If your goal is privacy, almost any reputable private engine is a strict improvement over a profile-driven default, and the switch costs nothing. If your goal is different results — escaping one company's ranking — you specifically want an engine with its own index, which is rarer.
Try it as your default for a week before deciding. Search habits are sticky, and the honest test is whether you find yourself reaching for the old engine. A per-site fallback (a keyword that queries another engine on demand) removes most of the friction.