It depends on what the app does -
1. Picture containing apps may duplicate the photos some of which may remain after other images are transferred
2. Same thing can happen with notes or email
For example my text tones mysteriously stopped - and I had to completely restore to get them working again on my phone
At times restoring the backup brings back the issue (typical example restrictions password) - this is where the conclusion is that something in the content is causing it - and a factory like install of the iOS downloaded fresh from Apple servers would be needed to workaround the issue
It is a little bit vague but also dependent on the issue at hand - so please feel free to ask for clarifications if you need them
Of course some of my esteemed colleagues on the board may also chime in with their perspectives