I use Firefox now because I care about privacy, and I'd rather use a browser developed by a non-profit that cares about that as well. But I suspect that's a bit too abstract for most people to care about, at least at this point.
Chrome's advantage seems fairly baked in; people aren't going to shift unless there's a decent reason to. I wonder what that reason could be. Can privacy concerns become a sufficient motivator for people to shift browser; or even, thinking a bit bigger, to change the fundamental architecture of the web?