Premium Economy is essentially a section of seating between the Economy Class and Business Class. Business Class offers more legroom and recline than Premium Economy. While you get better food in Premium Economy than that served in Regular Economy, Business Class offers gourmet meals and finer wines.
Premium Economy offers wider, more comfortable seats than regular Economy, while Business Class generally offers flat-bed seating and a fully dedicated cabin. Also, the service is better in Business Class as compared to that in Premium Economy. The best way to score a deal is by looking for last minute Business Class tickets.