The regional and popular differences in the United States are pretty striking. We are a large country with over 300 million people living in our borders, and surprise, surprise, we don't agree on everything (or much) or value the same things.
So when Bush is President, many of the people in Massachusetts or Hawaii dislike the policies of the national government. With Obama President, the same could be said of Utah and Alabama. So you take a large society with this many different and competing values and you'll see controversy over state vs. federal power.
Five years ago it was lawsuits about the Patriot Act. Now it's lawsuits by states against health care reform law.
On the proper balance between the national government and the states:
I can think of a couple of reasons for controversy on this issue. First, freedom: If your state government enacts a policy that prevents you from making a living in the way by which you are accustomed, it is fairly easy for you to move to the next state. If the national government enacts a policy that prevents you from making a living in the way by which you are accustomed, it is more difficult and expensive for you to move to another country. So, the more policy fields that are left to the state governments and the fewer that are given to the national government, the more freedom to choose, each individual has.
Some people are not happy unless they have power and control. They would prefer national power so that it can be used to limit how you make your living, or how you recreate (no gambling or no alcohol), or how your health care institutions are organized. Other people are happy just to be left alone. They would work to limit the amount of power that can fall into the hands of one person or one party. They would prefer state power.
There are people who like central government. From the beginning of government under the Constitution of 1789, the people who made their living by manipulating stocks and bonds and certificates and national debt, wanted a strong central government so that they could manipulate these forms of imaginary wealth from one power base and not have to do their manipulating from 13 (then) or 50 (now) separate power bases. There are also groups of people known as progressives, liberals, and neo-conservatives. These groups want to enforce their ideas of morality and social order upon everyone, and they think they can better do that if more power is in the national government and they control that power. They know that it would be harder for them to control 50 different state governments with power over these issues, so they want the power over these issues to be in the central government where they hope to have easier influence.
Also, within each state, there are interest groups that find that they will be better off if they can control certain of the state's issues and policies and institutions and resources, than if these are controlled from Washington. And there are national interest groups that would be better off if they could control some of these issues, etc., in all states, from Washington.
If governmental power is dispersed and diffused amongst 50 state governments, it is practically impossible for one man or one party to capture all of that power and use it to rule all of the rest of us tyranically. If governmental power is concentrated in one national government, men and parties will strive very hard to capture that power for themselves, and we will thereby, someday, sooner or later find ourselves without much freedom.
Second, quality of government: If 50 different governments have laws regulating use of mood altering drugs, the laws of some states will be better than others. As these better laws are recognized, more states will adopt them so that better drug laws gradually come into being throughout the country. If only the national government is allowed to have laws regulating use of mood altering drugs, the whole nation is stuck with what ever those laws are, be they good or be they bad and most likely they will be bad.
I would say that the main reason why this balance has been controversial is that the idea of tyranny by a central government is a major concern in our history -- it is what we became independent to escape from. Therefore, it is easy to get people upset when they feel that the central government is getting too much power.
This has also been a major issue simply because the limits between the two levels of government are not clearly defined. The Constitution is ambiguous on the question of how much power the states should have.
Finally, I think it has remained controversial because our states are still fairly different from one another. We have very different ideals (in some respects) in, for example, Idaho and Massachusetts.