Which event had a greater impact on federalism: the Civil War or the Great Depression?
There is a very good argument to be made for the notion that the Great Depression had a greater effect on federalism than did the Civil War. The other answer posted here succinctly points out the vast expansion in the role of the federal government that resulted from the Great Depression. President Franklin Roosevelt's New Deal programs injected the federal government into the economy to an extent previously unseen. Jobs programs like the Civilian Conservation Corps and the Public Works Administration; regulatory structures for the financial services and banking industries such as the Banking Act of 1935, the Emergency Banking Relief Act, and passage of the Glass-Steagall Act; unemployment compensation through the Federal Emergency Relief Administration; and other programs all expanded the government's role in the private sector. To that end, it is logical to conclude that the Great Depression had a greater impact on federalism than did the Civil War.
The above argument for the Great Depression as more influential on federalism than the Civil War aside, it is difficult to conclude that the latter event did not have a greater impact. The debate over federalism had its origins in the nation's founding during the eighteenth century. That delegates to the Constitutional Convention were unable to resolve that debate marked an early and extremely important failure on the part of federalists to ensure the survival of the Republic. The federalism versus anti-federalism dispute led directly to the outbreak of war between the North and the South in April 1861. The Confederacy's defeat marked a defeat for those who had agitated for a minimal role for the federal government in the nation's conduct. The Union's victory, conversely, cemented the federal government's status as the supreme power in the nation—a principle specified in Article VI of the Constitution. New Deal programs certainly expanded the central government's role, but the Civil War militarily ensured that the supremacy of the federal government survived.
This is, to some degree, a matter of opinion as we cannot accurately measure the amount of federalism that existed before and after each of these events. My own view is that the Great Depression had a greater impact on federalism, particularly in the long term.
The Civil War did have some impact on federalism, particularly in the short term. After the war ended, the national government essentially ran the states of the South. The Constitution was also amended to deny the states the right to legalize slavery. In this way, the war led to a situation where the national government had more power than it previously had and the states had fewer options.
However, the Great Depression really changed American government in a fundamental way. Before the Depression, the federal government was not really involved in the economy to a great degree. With the New Deal, all this changed. The federal government came to be involved in practically every aspect of the economy. It started to do things like insuring bank accounts, providing income to people after they retired, and funding projects to bring electricity and irrigation to rural areas. The New Deal brought about a huge change in our governmental system in a way that the Civil War did not. Therefore, I would say that the Great Depression had a greater impact on federalism than the Civil War did.