America is dramatically more violent than any other industrialized country, as determined by its rate of assault deaths (guns, stabbings) per 100,000 people. Still, America's assault death rate is rapidly dropping (thought still very high), and the number of gun owners in America is also steadily declining. Studies show that banning assault weapons does not at all affect America's violent crime rate.
But banning assault weapons would affect America's mass murder shootings. The weapons of choice of the mass shooters were overwhelmingly semiautomatic handguns and assault weapons.
Of the 61 mass murder shootings in the United States since 1982, in only 11 of them were weapons used that were illegally obtained in 49 instances, the weapons were legal.