Hoover was a good man but terrible, terrible prez. One more year of how things were going under Hoover & there would have been a Communist Revolution in the U.S...no kidding, when do u think all those ppl busted in the late 40s got their ideology. The US Communist party had 2 million members, others were emigrating to the USSR. The West & Midwest were on the verge of serious riots. FDR saved capitalism.
I agree that FDR saved capitalism by taking, or giving the appearance of taking, effective action to improve the economic climate. Hoover gave the appearance of inaction in the face of conditions that were so bad that people demanded some type of action. If something hadn't been done, people would have turned to something more drastic, like communism.
Having said that, I think that the New Deal made long term changes in the way the economy operates much more than giving a short-term economic boost.
The two big measures that come to mind are deposit insurance for banks and Social Security. The deposit insurance was enacted in the first 100 days, and effectively stopped the severe banking crisis, allowing some type of normal banking activity to resume. That didn't cure the depression or bring about the return of prosperity, but it took the edge off and had a long term impact (mostly, but not all, good). Social security was an economic drain at the outset because taxes began in 1937 but payments did not begin for several years after that.
Many other New Deal measures were boondoggles, or were short-term and ineffective. The New Deal in the long run did little to end the depression, and many of the Roosevelt policies and mentality could be said to have prolonged the depression. The depression really ended with the gearing up of war production in the 1940-41 period, but even here, the companies responsible for defense production would not agree to make the investments necessary for large-scale production until Roosevelt agreed to revise some of his anti-business policies. The fact is that Roosevelt's class warfare, and the policies that flowed from it, scared business off from investing and prolonged the depression. His own wife told him that.
In short, Roosevelt wins because he promised to do something, while Hoover largely promised nothing. In desperate situations, something, anything, will win over nothing.