The difference between a funded mandate and unfunded mandate in the private sector is, for example, the difference between requiring your kids to go to private school or requiring your kids to pay for their own private school.
The difference between a funded and unfunded mandate in the public sector is, for example, the difference between the federal government taxing citizens and giving that money to the state to implement some educational reform, or the federal government telling the state it has to do the taxing itself. Either way, the people have to pay for the reform.
Sure, this ignores redistribution amongst the states. Zero-sum game => I don't care. On the contrary, most of the time I'd rather the burden of a project be squarely on the shoulders of the ones benefiting from it. People make more careful choices when they have to pay the consequences.