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.