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Assuming that by saying privacy, you mean "not being tracked and identified uniquely", then you should know there are two elements to this and both are really important. The fingerprint and the IP. To have privacy you have to eliminate both vectors. One alone is not enough. The fingerprint is technically more important, but still the IP is an extreme isolator. So, both essentially have to be addressed or the effort is mostly futile.
Secondly, know that one browser is generally not enough. No matter which privacy browser you use you will eventually run into that website that just doesn't wanna work with privacy features enabled. Detecting what to turn off can be tricky, time consuming, and sometimes futile. Long story short, to have less headache you always need an extra vanilla browser at hand just in case.
IMO, best browsers for privacy in order of effectiveness are:
- Tor
- Mullvad
- librewolf
- and brave
However again, without the IP solution they really don't help you.
Tor i dont recommend for general use for the average person cuz you can run into compatibility issues often and just doesnt work for all uses. However it does address the IP issue by default without the need for a vpn. Brave is more compatible and "comfortable" with websites than the other three but its really not as good against fingerprinting. And again you still need a totally vanilla one cuz even with brave I have run into problems.
So i personally stick to Mullvad as my primary private browser (for a multitude of reasons), Brave as an intermediary, and vanilla Firefox as my vanilla (though you could pick whatever you want). With a vpn. Each have their use case, and together they offer what you need.
Remember, the IP problem has to to be solved too otherwise you're still strongly isolated and identified.
See also this thread:
https://discuss.grapheneos.org/d/6854-desktop-browser/6