Chrome can't properly compete privacy wise, same as Google in general can't. Privacy will be an issue, and increasingly so. Personally, I never understood Chrome hype, though I admit, that Mozilla's focus on FirefoxOS was distracting, and slowed down their desktop progress. It's good they are back on track now.
Do you really believe that? The way I see it, most people just don't care. At all. Else they wouldn't sell their souls to private companies (e.g. Facebook and Google) without a second thought and we'd see more outrage against government surveillance that's being pushed in nearly every country all over the world.
Firefox is unlikely to gain much of a market share with only privacy-focused changes. People care about ease of use and especially performance. FF lost a lot of market share due to its horrible performance, compared to Chrome.