What does a duke do vs a prince?

All of the Royal dukes I can name: the Duke of Edinburgh (Prince Philip); the Duke of York (Prince Andrew); the Duke of Cambridge (Prince William); along with the Dukes of Kent, Gloucester, and even Prince Charles (as Duke of Rothesay and Duke of Cornwall) are both Dukes and Princes, so the question is a non-starter.

There are non-Royal Dukes (the Duke of Norfolk, the Duke of Bedford.......) who are hereditary peers of the Realm, and carry out duties as such, but obviously do not carry the HRH title.