Eduard's answer is fully correct. Not the default browser is saving default apps, the system does.
However, you can get default app settings for any Intent like this:
public static void getDefaultApp(final Context context, final String url) {
Intent i = new Intent(Intent.ACTION_VIEW, Uri.parse(url));
ComponentName component = i.resolveActivity(context.getPackageManager());
if (component == null) {
// no app at all can handle this intent
// there might be profile restrictions applied since android 4.3
} else if (component.getPackageName().equals("android")) {
// there are multiple apps available handling your intent
// no default app is set, the Chooser will be shown
} else if (component.getPackageName().equals("com.android.browser")) {
// the default browser will be shown
// there might be multiple apps installed handling your intent
// however the user picked the default browser
} else if (component.getPackageName().equals("com.android.chrome")) {
// chrome will handle your intent
// there are multiple apps installed handling your intent most likely
// however the user picked this app
} else {
// some other app will handle your intent
// there are multiple apps installed handling your intent most likely
// however the user picked this app
Log.d(TAG, "user choice package: " + component.getPackageName());
Log.d(TAG, "user choice class: " + component.getClassName());
}
}