Fascinating that Virginia got final jurisdiction for treason to me because the place John Brown attacked was the Federal Armory in Harpers Ferry, one of only 2 in existance at the time in the USA. Plus, President Buchanan had ordered Colonel Robert E. Lee and the marines to Harper's Ferry as soon as word got to Washington.
Brown planned on using these weapons to arm the slaves that were going to supposedly heed his call for armed insurection and rebellion. Problem was, none (or just a couple) of the slaves joined him and he murdered more who didn't join.
So back in the day, the Federal courts allowed the States to handle treason. Too bad we can't get Pelosi extradited today.
I don't think that Virginia got final jurisdiction, they got initial jurisdiction. I suppose it is possible that if Brown had been acquitted, or sentenced to time in prison instead of hanging, the Federal government might have tried him as well (I haven't checked the ante-bellum Federal Statute books for a Federal treason statute).
Brown was intending to overthrow the entire United States' government, and all the State governments. He had in his possession (back at the Kennedy farm, if memory serves) of a new draft Constitution of the United States, that he and his accomplices had drafted in Chatham, Canada West in the summer of 1858. Virginia was just the first place he intended to overthrow. Maps, also recovered at the Kennedy farm, showed his planned area of operations: Alabama, Florida, Georgia, Kentucky, Louisiana, Mississippi, South Carolina and Tennessee, with symbols on counties with large black populations. He was not just trying to run off slaves. When he said that before his trial and when his supporters said so in front of Congress, they were lying, and they knew they were lying.
On a relevant sidenote, in Kentucky vs Dennison, the Ohio Attorney General advised Gov. Dennison not to extradite a criminal to Kentucky because slave-stealing wasn't a crime in Ohio, even though the Constitution clearly says that the criminal will be delivered up to the State having jurisdiction over the crime. This was just another example of how northern Republicans were probably going to run things, once they got in power. If I were a Southerner in 1860, even a non-slaveowning Southerner, I'd be very nervous about such a bunch being in charge of the Congress and the White House.