Answer:
A major difference between the two is that Herbert Hoover was much less interventionist than Roosevelt, intervenionist meaning a person who believes the state should intervene the economy in order to fix it, instead of leaving all economic solutions to the market alone.
Hervert Hoover only reluctantly applied some interventionist policies to try to end the Great Depression: for example, signing the Agricultural Marketing Act of 1929 which allowed the reduction of crop surpluses that were a cause of farmer's economic ruin. But beyond a few other measures, there's not much else to his presidency. He did not even end Prohibiton for example.
FDR on the other hand, gave a lot more power to the state. He implemented a series of reforms known as the New Deal, with the aim of ending the Great Depression. He also ended Prohibition, and led the country during World War II.
In general terms, most historians coincide that Roosevelt was a much better president than Herbert Hoover.