I decided to compare the performance of teams in their promotion season to their prior season in the Championship to measure the difference in quality between both leagues. Going back to the 1993-94 season, 53 teams have been promoted from the Championship (or First Division as it was previously named) to the Premier League. The table below shows the average changes in points and goals after promotion:
A little less than half of the promoted teams were relegated after one season. These teams had an average goal differential of 0.67/match in the Championship but this dropped to -0.48/match in the Premiership. Net change was 1.15 goals/match worse than the Championship season.
So can we say that teams from the Premier league are 1.15 goals/game better than their Championship counterparts? Maybe so but since we are comparing results from one season to the next we have to account for changes in players, changes in management and changes in spending. Currently a promotion to the Premier League is estimated to provide about £90 million of additional income to the promoted teams. How they choose to spend that money can have a big impact on their performance.
However, the impact of those factors (players, managers, income) is hard to quantify. So more work needs to be done in this area to refine this, but for now I'm using the 1.15 goals as a yardstick to differentiate the quality levels between the leagues.