Benefits: It guarantees a minimum income for any employee in the country. Also, since there's only one set of laws, it's easier to legislate, maintain, enforce, and comply with.
Drawbacks: The minimum wage needed to survive depends on where you live. It's much cheaper to live in Little Rock, Arkansas than it is to live in New York City. By setting the standard for the wealthier areas, it places undue strain on the poorer regions.
Minimum wage laws are a good thing, but they need to be regionally based. The federal government can set a legal standard that each state must adhere to and that'd work. For instance, stating that the minimum wage must allow a person to make at least half of the median or average income in their state, whichever is greater, would be a simple law to create. Each state would have the minimum standard to adhere to, and they'd always be able to improve as needed.