Theoretically, there are defined powers that are given by the Constitution to each level of government. The federal government, for example, is the only level that has the right to regulate commerce between states. The states, on the other hand, have the right to legislate in basically any area that is not specifically given to the federal government.
But there is plenty of gray area and that is where the arguments between state and federal governments tend to fall. For example, how much can the federal government do under the heading of regulating interstate commerce? This is something of a hot topic right now because of the new health care law. May the federal government come out and tell people that they must buy health insurance? It is not really clear whether this falls under "regulating interstate commerce."
Because of this sort of ambiguity, there is plenty of room for the two levels of government to argue over their respective powers.