Is the Progressive Era best understood as an era of the expansion of democratic society or as an era in which middle classes attempted to exert social control?
It is better to understand it as an attempt by the middle class to exert social control. This aspect of the era outweighs any moves towards more democracy that occurred.
There were, to be sure, attempts to increase democracy during the Progressive Era. Women got the vote and Senators came to be directly elected by the people. In some states, initiatives, recalls, and referenda became legal. However, all of these increases in democracy were truly meant as ways to increase middle class power and reduce the power of big business and political machines.
In addition, there were many reforms during this time that cannot be seen as democratic at all. The most important of these, of course, was the push for Prohibition. This was one of the greatest attempts at social control in US history.
Since even the moves towards democracy were aimed at increasing middle class power, the Progressive Era is best seen as a middle class attempt to exert control.