My suggestion would be to use a combination of Mixpanel (for detailed, granular data) and Facebook analytics (for the strongest demographic data).

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.