When to save data to database, onPause() or onStop()?

When to save data to database, onPause() or onStop()?

Either. They are nearly identical, particularly on Android 3.0+.

If the activity that is taking over the foreground is a typical full-screen activity, so that the earlier activity is no longer visible, onPause() and onStop() will be called in rapid succession.

If the activity that is taking over the foreground is themed to be more like a dialog, where the earlier activity is still visible, onPause() will be called, but not onStop(), until such time as the activity is no longer visible (e.g., user now presses HOME).

Most apps aren't worried about the "themed to be more like a dialog" scenario, in which case onPause() and onStop() are called one right after the next, and you can fork your background thread to save your data in whichever of those makes sense to you.

However, in many places of android documentation they always suggest not doing heavy work (such as writing data in database) in the onPause() method as it will delay the transition between the activities.

The same is true of onStop(), as both of those methods are called on the main application thread.

So, is it OK to assume that any Android device (including different ROMS) will ensure a call to onStop on the activity?

Both onPause() and onStop() will have the same characteristics from the standpoint of process termination. Either both should be called (normal case) or neither will be called (e.g., you crash, the battery pops out the back of the phone).

And this is the best place to make any time consuming storage writing of the App?

Either onPause() or onStop() are fine places to trigger the work, done on a background thread, to persist your data. If you prefer to do that work in onStop(), you are absolutely welcome to do so. Personally, I'm an onPause() kind of guy.