State prosecution is in a court run by a state, or a subdivision of a state like a county or city. It is under state law, and the judge and prosecutor are employed by the state.
Federal prosecution is in federal court, under federal law. The judge and prosecutor are employed by the federal government.
Most criminal prosecutions are in state court. Federal law is, at least in theory, limited to federal concerns; interstate trafficking in drugs or firearms, robbery of federally-insured banks, federal tax offenses, and so on. In practice, many state crimes could be charged in federal court, but the federal prosecutor chooses not to. Because federal criminal penalties tend to be more severe, and because the same conduct is rarely prosecuted in both state and federal court, it is usually in the defendant’s best interest to stay in state court.
Because there are fewer federal prosecutions, everyone involved has more time. The attorneys spend more time preparing for trial and preparing written motions, and the judge has more time to consider the issues. There is less pressure to move the case through the system. But, because the federal criminal penalties are so severe, and because federal prosecutors rarely bother with weak cases, federal prosecutions are even more likely than state prosecutions to be resolved by a plea bargain rather than a trial.
