Progressives prefer coercion over competition. They believe better outcomes will be achieved by a stronger central government forcing everyone to do what that government says is "right" than by a wide variety of solutions being attempted by many different groups to see which ones are more effective.
Progressives generally do not prefer a strong central government because they are truly enamored of strength or strong man, per se. They prefer centralized solutions for society's problems because they genuinely believe that is the best route to a solution to those problems.
Conservatives, on the other hand, do not believe that centralized strength is the most effective way to solve problems. Instead, they assume that solutions will not be obvious, even to well-educated experts. They believe that the shortest and most effective route to effective solutions for societies problems is competition among a large number of potential solutions.