Franklin Roosevelt's philosophy of government represented a sharp break with the past. While Hoover is often vilified for not doing enough to stave off the effects of the Great Depression, he was behaving within what was the normal understanding of the role of the federal government at that time.
Up until Roosevelt, the role of the federal government was understood (with a very few exceptions) to be to handle national defense and administer the laws of the land. Social welfare programs by and large were not part of the scope of the federal system. If Minnesota had a high unemployment rate and people there were going hungry, that was a problem for the state government to solve. If New York had a lot of poor elderly people with no money eating out of garbage cans, that was their problem.
FDR's philosophy completely reenvisioned the federal government's role. He advocated for big government programs to be coordinated in Washington to systemize aid and get the help to people and businesses that they needed to survive and start over. He knew the states couldn't do it, because they were broke. He knew the business sector couldn't do it, because it was broke.
This new federal system proved to be more efficient than piecemeal efforts by the states. FDR then worked to put in a permanent safety net so that the federal government would always be there to catch the economy when it went into free fall. He wanted to ensure that it would never crash so totally again. He wanted the average American to have what he and other rich people had: the knowledge that even if things went bad for them, they wouldn't starve, wouldn't be homeless, and wouldn't be crushed and forced to beg for the necessities of life.
Hoover, however, adhered to his "hands off" understanding of the federal government's role in social welfare after the 1929 crash. He expected the business sector to bounce back and pull the national economy up with it. While he did try to pump some federal money into propping up the economy, his philosophical approach was such that his attempts were the proverbial band-aids on deep wounds. He was a good man, but not a visionary, and in the 1930s, the country needed a visionary.
Roosevelt came into office boldly, willing to try almost any experiment to save the economy. He fully grasped that it was near death and that normal methods were not going to revive it. He grasped that the business sector was so flattened that it could not jumpstart a recovery. He forever changed the way we view the federal government's role in the economy.