Firefox has been my daily driver for 2-3 years now. I’d switched to Chrome several years before that but when FF fixed its lag issues I went back right away.
Mozilla overplay the “not for profit” card but with Google you can be sure they are collecting and archiving absolutely everything that passes through their servers.
Assuming that one switches to Google as the default search engine (I'd love to know how many do - additionally I beleive Google is the default outside the US anyway), there's effectively no difference. Neither browser does anything special wrt privacy, the same resources and scripts are loaded in both. Safari are the only browser brave enough to try anythng more exciting in this area. (OK, Brave are also in this area, but they're not of much significance right now.)
Sure, Firefox's private browsing does offer tracking protection. But most "normal" users don't seem to use that. And some would argue there's little value in blocking tracking in a session that will be wiped anyway.
One can assume Google is tracking a ton of data beyond just what Google searches users do.
Firefox users who pick Google as the search engine are still giving a lot of info to Google, but less info than Google would have had if the user was using Chrome.
Citation needed.
Google Analytcs and ads are so widely that most of your browsing will be tracked regardless of browser, even regardless of your search engine (but the search engine is also quite major since they can track what you were trying to search for before jumping into the web).
But there's also a privacy policy explaining what chrome actually sends: https://www.google.com/intl/en/chrome/browser/privacy/
It is worth mentioning Chromium is open source too.