The conventional wisdom is that the national government is best suited to serve national needs, particularly when states either lack the resources to provide those services or when a state might not be able to financially provide those services. One example is national defense. It's applicable to the entire nation and it's something that no single (or group of) state(s) could do on their own. Another example is the interstate highway system--which, interestingly, is the Interstate and Defense Highway System.
On the other hand, state governments are better suited to serve the needs of their own citizens, especially when those needs might differ from other states. (In addition, of course, the Constitution says that those powers not specifically given to the federal government are reserved for the states.) Education is a service that generally is considered primarily a state issue.
Today, a lot of major programs are blended, or are essentially a federal-state partnership. The funding of Medicaid, for instance, is one. (Look up some of the debate about Obamacare and the reluctance of some states to fully participate.)
But read the Constitution to see which powers are clearly federal powers.
Hope that helps.