Personally, I do not think things would be much different. The things that happened during the Progressive Era would have happened anyway, just not all at once.
However, to go along with your question, let me look at two things that might have been different.
First, I will say that government would have continued to be much more corrupt if there had not been a Progressive Era. Senators would not be elected by the people and would still be able to be "owned" by big businesses, for example. Big city machines would still exist.
Second, there would be much less organized crime. If there had been no Progressives, there would have been no Prohibition. With no Prohibition, the Mafia would not have gotten rich from bootlegging -- no Al Capone, no people like that.