Separation of powers.
Commit a crime on federal land (National Park, Indian Reservation, etc) and you are hauled into federal court (or possibly local Indian court). Commit a crime on state land (state, county, city, etc) and you go to state court.
Fed versus state law is not a separation of powers issue. State law does not trump federal law. Federal law is not limited in jurisdiction to only land areas "owned" by the federal government. Federal law can be enforced and is applicable anywhere in the United States. If that were not so, the DOJ and the FBI and the dozens of alphabet agencies such as the IRS, FAA, FDA, DOE, SEC, and FEC would have no standing anywhere but in national parks and on Indian reservations. And illegal aliens would be "illegal" only in those areas. Sounds like you were not educated in America, as a graduate from a U.S. high school would be required to know this.