From the first link, which goes to a U.S. News article:
[T]he U.S. attorney's office in the Northern District of Illinois maintains that federal weapons law enforcement is among the top priorities of their office. "We have a number of different methods of attacking gangs, guns, drugs and violent crime," says spokesman Randall Sanborn, who notes that many gun arrests are reviewed to determine whether the arrest should stay with the county or be brought to the federal level. "We look at which court the defendant is likely to get a substantially greater sentence... More cases that used to be brought federally are now staying in state courts because [they are] now able to get a sentence equally great or greater," he says....So Chicago ranks last in federal prosecutions because there's more state law regulating guns and there's more enthusiasm among state prosecutors about enforcing it. Street-level violence is more properly handled in state court. Unless you've got interstate webs of criminal activity, gun crimes shouldn't be cluttering up the relatively scarce federal district courts (which have to handle civil and criminal cases). What seems to be happening in Chicago is a preferable allocation of federal and state power.
While the districts that ranked lowest last year for federal gun crime prosecutions all contained major cities, the districts at the top of the list for its enforcement were almost exclusively rural. The districts of Southern Alaska, Kansas and Western Tennessee ranked first, second and third in prosecutions of federal weapons laws per capita last year.
Susan Long, a statistician and co-director of [Transactional Records Access Clearinghouse, which tracks federal data], said the data revealed a stronger federal enforcement presence in rural areas than urban ones. "If taxpayers of [a certain area] don't pass strong gun control measures ... the feds pick up the ball," she said.
The reason other areas have a higher proportion of federal gun-crime prosecutions seems to be that there's much less state-level enthusiasm about gun crimes and the feds are stepping in to fill the gap. Depending on what crimes are prosecuted, you might want to criticize the feds for oppressing the people in the states that — following their vision of government — have a more easygoing attitude about what people do with guns (perhaps because people around them aren't doing such bad things, as they are in Chicago). But you've got to perceive the way these sparsely populated places are getting proportionately more prosecutions and thereby driving places like Chicago lower on the TRAC list of federal prosecutions rankings.