The major benefit of this change is that both the federal government and the state governments can now attack various problems. We can see this, for example, in the field of education. Cooperative federalism gives the national government the ability to participate in making education policy, but the states still have the power to do things on their own. This puts more perspectives to work on a given problem.
The major disadvantage is that there is now much less in the way of state power. With cooperative federalism, there is not as much room for states to be sovereign. The federal government reaches into more and more areas of policy that were once reserved for the states.