This question is actually addressed directly in the Constitution. The Supremacy Clause (article 6, clause 2) explicitly states:

This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.

What that means is that when federal and state statutes come into conflict, federal law automatically overrides state law — as long as the conflict relates to one of the 'Enumerated Powers' set out in Article 1, Section 8 as being explicitly delegated to the federal government.

The Tenth Amendment codified the idea of states' rights:

The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.

That means that state law takes precedence in any issue reserved to the states. In practice, however, it's much more complicated, thanks to wildly varying interpretations of how any given statute relates to the enumerated powers and the Tenth Amendment.