My guess (not having used the Amazon store however) is that Android's permissions system is hurting it. Why does that app need location and full network access? So you become suspicious. And so on. While on iOS its automatically given full rights apps get, apart from location, which it asks for at runtime, not install time. So while the iOS app has as much ability to start feeding data home, the fact that the Android app is forced to admit it uses network access leaves us more suspicious.

It doesn't help that many apps have a perfectly legitimate purpose for that network access, to download and display ads.