Firefox private browsing is implemented almost identically to Chrome incognito mode and will not offer any meaningfully better privacy. Both will not save cookies and browsing data locally, but both can be tracked by the remote sites you access.
Firefox won't implement cohort user tracking. if they do, probably not in incognito like chrome, which just sets a new set.
Firefox doesn't preload hundreds of links from the page your reading, using google's dns serves despite your dns settings.
so many reasons that people here just ignore and pretend they know anything at all about browsers today.