The back button isn't that great in Android. I'm never sure if back is going to take me back to another screen or out of the app completely. Sometimes if the app is launched from another app pressing back doesn't take you back to the originating app.
As an iOS and Android user the Home button is still my favorite. It's what I'm used to and for the most part they work the same on both platforms.
The back button should follow the users path; if I'm in an email, then a click a link, and then get an SMS then the back button should take me from the SMS message, back to the browser, and then back the email.
However, applications need an additional bit of UI so that from the SMS message you could go "back" to the list of all messages, etc within the app. It sounds like, on Android, there is some confusion between these two use cases and other issues that make it unreliable. It's a shame because the concept is sound.
As an iOS and Android user the Home button is still my favorite. It's what I'm used to and for the most part they work the same on both platforms.