So with the recent Bing situation I wanted to take a second look on private search engines and sharing my conclusions of each search engine. Here is my list of private search engines:
I really like Duckduckgo, it has all important tools, decent result quality and a great image search function. Instant answers is very useful. My main problems are the reliance on Bing as the index and the choice of Apple Maps as mapping solution. Apart from the situation with the browser and Microsoft tracking Duckduckgo has a pretty clear record and the privacy.
Startpage is another great option. Apart from mapping everything is there and, while not as good as Duckduckgo's, the image search engine good. The results are based on google and on par to better than those of DDG. The main advantages over DDG are European base (Netherlands) and the anonymous view, which basically functions as a quick access VPN, but sadly breaks ad/tracker blockers. Privacy for regular search is equal to DDG, but you have to disable JS to get rid of some telemetry. It is owned by an advertising company
Swisscows is okay. It is also Bing based, but slightly worse than DDG results. It lacks image search filters and mapping, but offers a music search which allows you to listen to ad free music. It also has an anonymous view, but it's not interactive. Privacy is similar to DDG, but has more telemetry and (temporally) stores your IP. It is from Switzerland, it also has a very strict anti gore/porn policy that sometimes makes normal search terms inaccessible.
Qwant used to be very solid French search engine, has dropped in quality. Similar search quality to DDG, image search like Startpage. They use Bing in combination with their own index. Then problems: They share your IP with Microsoft and they replaced their main advantage, openstreetmap based independent mapping service, with AI summary's that require an account. Worse privacy than all the above.
Very similar to DDG. The main differences are that Ecosia is based in Germany, it plants trees to fight climate change, but also forwards your IP to MS.
Braves main advantages are being independent, both with the search and the AI, and the goggles that allow you to customize your results. Search results are slightly better than DDG, image search is bad, no mapping is available. Brave has had invaded privacy in the past, but currently the privacy is good as long as you disable statistics. The company itself is a bit concerning and the CEO is homophobic.
SearXNG is self hosted and open source, it uses various search engines as index and has a ton of extra feature like music search, fediverse search and a bunch more. While it has the most features and best privacy of all options, public instances are sometimes slow and the results aren't really good.
Kagi is in principle a decent quality search engine, but it is paid and has some problems that are only getting worse. For those interested read this blogpost.
4get is a open source, self hostable search engine. It acts as a web scraper for various search engines, also supports Soundcloud. It has great privacy and good results, but it lacks mapping and the official instance requires a CAPTCHA per 100 searches
Yep is an independent search engine. It is private and has good results, but lacks image search tools, video search and mapping.
Decentralized independent search. It has good results but lacks image search tools, is sometimes unreliable and has intrusive advertising
A quick fire round of search engine that have decent privacy, but I wouldn't use due to result quality:
Ekoru Like Ecosia, but for cleaning oceans, Bing based, few features, requires extension.
Whoggle Like SearXNG, but with less features.
Metager Meta search engine with multiple search back ends, mainly Bing (Yahoo), completely powered by renewable energy
Mojeek Independent UK search engine with few additional feature, is supposed to be unbiased
AstianGO Slightly modified version of LibreX by the Devs of the Midori Browser
Ghostery German independent search engine, regular web only, offers tracker analysis for websites
Stract Open source, self hostable, independent search engine
Lilo Like Ecosia, but with fewer features and the option to support various projects
YouCare Bing based search, shares your IP with MS, does "good deeds", some missing features
Giburu Google based proxy search
Gigablast Open source, self hostable, independent search engine
Mwmbl Open source, independent, self hostable search engine. Only web results
Marginalia Open source, independent, self hostable search engine. Only web results, offers filters
That would be my list. I'll still be sticking with Duckduckgo but I'd reconsider if Startpage improves it image search. Brave will probably never be my default, but it has proven it's role as a more private backup. Comment if I missed any search engine
Search engines I didn't include due to horrible privacy Bing/Google/Yandex/Yahoo/You/Baidu
Have you looked at this ?
https://seirdy.one/posts/2021/03/10/search-engines-with-own-indexes/
This doesn't just cover what the title says, it also shows who uses what indexes. It's the most comprehensive list I have seen.