Compared to Chrome, Firefox has the huge advantage that it is Free Software, while Chrome (the whole package) isn't.
Compared to Chromium (the Free Software part of Chrome), Firefox has the advantage that it has no anti-features in the first place, rather than having the Chromium community trying to keep after Google removing each anti-feature as soon as they notice.
Mozilla is an independent advocate for the open web, compared with a for-profit entity. This means the incentives are better. They try to fight the good fights, even if they don't always succeed.
Both browsers communicate with their owners under various circumstances. Both have it relatively well documented (both with some omissions, as the docs lag behind). Both had screw-ups (probably, non-malicious but just accidental - YMMV) and were caught communicating something (IIRC, non-severe) when they shouldn't have been. Both have their own ecosystem/services (starting with Google and Firefox Accounts respectively) that they actively promote.
This is subjective, but I believe in the large picture neither of browsers has some consistent technological advantage in terms of user privacy (fingerprinting, data leaks, options to block unsafe modern stuff etc). One or another wins over specific cases or introduces some measures before another does, but they feel to be generally on par - at least if we consider available extensions (adblocking, etc) and not just the core features.
The only significant difference I see is that one of the browsers markets itself with heavy use of term "privacy", and other doesn't.
Sure, but isn't it a variant of ad hominem? Or, well, ad collegium.
As long as Chrome itself really doesn't do anything particularly wrong, of course. But I think Google (probably because of lots of various rumors) went to great lengths to actually describe what they do and what they don't, and I haven't spotted anything particularly alarming in their privacy whitepapers.
Compared to Chromium (the Free Software part of Chrome), Firefox has the advantage that it has no anti-features in the first place, rather than having the Chromium community trying to keep after Google removing each anti-feature as soon as they notice.