Anyone can do better than Google when it comes to privacy, especially if you define "privacy" as "don't do what Google is doing". It is almost a tautology: we first define Google as the opposite of privacy and then market yourself as private by not being Google. In order to drive the point, you add some kind of blocking feature and, yay, private!
In order to be relevant, you need to do more than that. Firefox used to be a great browser not because it was private, but because it was a great browser. It had great support for the latest web technologies, tabbed browsing before IE, it was fast, etc... And because of that it managed to make a dent in IE market share. But now, what does it have that Chrome doesn't besides not being from Google? Firefox even lost most of its identity by discontinuing XUL (for good reasons, I know) and updating its UI to look more like Chrome. I use both browsers on a day-to-day basis and Chrome tends to work better on average, though Firefox seems to be slowly catching up. I don't know what the situation is with Servo but it might be what Firefox needs.
Another example would be DuckDuckGo. Again, it caught the "privacy" virus. Please, no, "private" just means you are a proxy for inferior Bing results in this case. The worst part is that DDG has more to offer than "privacy", like instant answers and bangs. Why not market these instead?