My suggestion would be to use a combination of Mixpanel (for detailed, granular data) and Facebook analytics (for the strongest demographic data).<p>Demographics is also something that you don't need a gigantic sample size like you would an AB test. So you can do something like present an incentivized (rewarded with in-app currency or an unlock or something) survey to some percentage of your users at random and you'll get a reasonable picture of your userbase.
Amazon just launched their own mobile analytics, wondering if anyone here had any first hand experience, how it would compare with google, what are you using?