Both sides use crappy and misleading statistics, which cannot actually have any logical conclusion drawn from them.
Once again, you cannot draw any kind of valid conclusion by comparing countries. Switzerland requires all male citizens under age 40 to keep a military assault rifle in their homes, and only recently limited ammunition so that they no longer need to keep ammo for it (though they can go buy some of their own volition). Murder in Switzerland is very low, and has pretty much always been low.
But South Korea bans handguns altogether, and rifles have to be kept at your local police department and checked out if you want to target shoot or go hunting. Guess what, murder is very low there, too.
Compare either of those to England, and what conclusion can you draw? None, because there is no logical connection. Comparing England to America is just as invalid, it's just the statistics sound nicer to some, and support a preconceived notion.
Here's a fun fact. Police in Germany estimate that illegally owned guns outnumber legal ones by 10 to 1. It's also pretty well-known that nearly all illegal guns are owned by neo-nazis. Would you sleep well at night if your police were telling you "yeah, the neo-nazis have us outgunned 10 to 1." Of course, neither crime nor neo-nazis are that big a problem in Germany.
Once again, crime, defined as actual violation of human rights, like theft, assault, and murder, is a social issue, not a legal one. Making theft, assault, and murder illegal do not prevent them from happening, nor do they significantly decrease the rates of occurence, because most people just aren't dick enough to do that to people (plus there'd be a fear of vigilante justice). How will banning possession of things that correlate to crime, but not cause it, help? If someone's already willing to kill, they'll be willing to get whatever weapon they want, even if they have to commit lots of crimes just to do that.