The relationship between federal and state constitutions is somewhat complicated.
On the one hand, the federal Constitution is superior to that of the states. No state can have a provision within its constitution that violates the Constitution of the US. For example, then, no state today could set up an established religion or allow slavery since those things are explicitly banned under the US Constitution.
On the other hand, state constitutions may go beyond the US Constitution in some ways. For example, a state may give more rights to a group than the US Constitution does. In the past, some states outlawed slavery before the US Constitution banned it. Today, some states provide more in the way of protections for gay people than the US does.
In these ways, state constitutions are inferior to the US Constitution, but may go beyond it in some ways.
I live in Ohio, and our SC has ruled our Constitution is a "Document of Independent Force".
While this is an Ohio case, it discusses what is known as the "New Federalism" concerning State Constitutions. It also discusses the Police Power and the Supremacy Clause.
This should give some good insight in answering your question.
Oh by the way, when the decision was written, the US SC had not decided the 2nd AM issue discussed therein, it has now.