If you use the simple method (Android Back up with your Google Account) you can restore settings and general app configurations (the restoration process actually just re-downloads your apps, doesn't really store the app files anywhere) but unless the app supports cloud back ups, app-specific data like game saves will be lost.
Only 3rd party back up tools like Titanium back up offer that kind of back up and restore. Note, however, that if you're moving from/to a phone with a different OS version (especially if it's a drastic difference, like going from Android 5 to Android 7), even those apps might fail as the app might be different or behave differently across versions.