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Both presidents were very successful, easily doing more in their presidencies than the majority of other executives that America has had since its founding. Before deciding on the winner of this category, however, I'll give a brief recap of the primary accomplishments of each president.
Roosevelt entered into office in the midst of the Great Depression and fought tenaciously to overcome the economic nightmare. To do so, he gathered enormous amounts of power and money to spread among the government, a process which would then inject that money into the sputtering American economy. The American populace was behind him every step of the way, desperate for any alleviation of the universal misery. The New Deal was possibly one of the largest and most comprehensive reforms ever instituted by the government, and it was almost entirely successful in giving people jobs, food, and shelter in the time that they needed it most.
Roosevelt's second accomplishment was so impressive as to inflict disbelief. The average man in America perceived World War I as a waste of lives and money, had forsaken the League of Nations since the very beginning, and wanted absolutely nothing to do with any overseas conflict, particularly in the midst of the worst economic conflagration ever seen. Yet despite this, Roosevelt did the impossible: guided American public opinion single-handedly toward the idea of rescuing Britain and France, created economic support programs to assist the stricken Allies against the worst threat the world had ever seen, and, finally, militarized in order to prepare the reluctant nation for the largest war it had ever participated in.
As for World War II itself, Roosevelt helped keep the fragile alliance of America, France, Britain, the Soviet Union, Canada, Australia, etc. together despite enormous differences in ideology, policy, and military planning. Without Roosevelt, it seems likely that the Allies could have lost the war, and we can be thankful that Roosevelt managed to live right up until we were solidly winning.
On the other hand, Truman finished the job and managed to bring the aggressive wartime economy back to the norm despite all odds. Strikes, riots, people believing him to be weak compared to Roosevelt... in spite of all these things, Truman put his foot down and would not let the United States spiral out of control. After things had cleared up, Truman's administration ended up caring over America at its absolute most productive and profitable time, an impressive achievement, to be sure.
Truman also had to deal with the hostility of Soviet Russia and the haunting possibility of World War III. Even though many believed that America had to push toward Russia immediately upon war's end, Truman decided that there had been enough bloodshed. With the Truman Doctrine of containment, he set the policy on the Soviet Union for decades to come, and thus averted direct conflict with Russia, the use of atomic bombs as a conventional weapon, and the possibility of World War III.
Truman's work on civil rights also made great strides, setting the roots for the future movement that would happen years later to secure fair rights for men and women of all races and colors. Despite the almost unanimous opposition to these efforts, Truman gritted his teeth and pushed on, believing that it was the right thing to do, even though he was personally as racist as the average man of the time period. What was just trumped his own personal feelings, and the success of the Civil Rights Movement owes a great deal of gratitude to the foundation laid by Truman's efforts and policies.
With regard to achievements in office, I regard Roosevelt as the winner of this category. It is hard to argue with any president doing so much. After all, Roosevelt overcame the Great Depression, prepared the nation for the upcoming global conflict, and essentially helped the entire world win World War II. By contrast, Truman's accomplishments involved finishing Roosevelt's work and cleaning up the mess. This sounds trite by comparison and was certainly highly important, but it just doesn't quite measure up.
Truman also set the standards for keeping us out of direct conflict during his portion of the Cold War and set the path toward civil rights. But these aren't exactly victories. Truman did not win the Cold War during his term, and he did not achieve civil rights for all; he just set the foundations for both. Roosevelt defeated the Great Depression and essentially won World War II. By the time Roosevelt died, victory was inevitable; it was just a question of how it would be done (atomic bomb or Japanese mainland invasion). And thus I believe that, in this category, Roosevelt is the winner.