Jurisdiction of Federal and State Courts
According to the principles of federalism and separation, each branch of power has dual control and subordination, which means that they are balanced between federal and state authorities. Judicial power includes correspondingly federal and state courts, which shape a balanced system together.
The main difference between state and federal courts is determined by their different jurisdictions. In other words, the types of cases, which these courts are empowered to consider, are different. States courts hear a wider range of cases than federal courts do, and these cases mostly consider more general crimes like robberies, thefts, traffic issues, family disputes and so on. However, if one party of the suite is the state itself, than such case will be under the jurisdiction of federal courts. In the same way, federal courts are obliged to deal with cases when certain federal, not state, laws are broken. Copyright and bankruptcy are also heard by federal courts.
Speaking about purely criminal cases, they can be considered by either federal or state courts, depending on certain criteria. The scope of state and federal legislation on a certain issue may differ significantly. In some cases, there is much more experience and records on a crime at the level of state legislation, so it is logical that this crime is considered by the state court. In case federal laws are more involved, the case is treated by federal courts. One should not forget that federal laws can be different for particular states within the US, so participation of federal courts is quite natural in such cases.
To sum up, jurisdiction of federal and state courts is different, though it might overlap for certain issues. Most generally, the use of either federal or state courts for a particular case is determined by what kind of law is violated.