to be honest, I believe the scientific approach would be for the person with the theory to come up with credible proof, or in this case a credible source.
as long as the source in question is anything that has to do with fox news, i doubt a good discussion with opponents who are willing to post their sources is ever going to be taking place here.
however, this is not a very easy debate even with credible arguments: there plainly are too many factors that can influence crime rates that the source did not provide data on. examples may be (but are not limited to): highier penalties, subsidies for education, and other factors that would bring down crime rates. You might be seeing the effects of more (effective) police activity for all we know.
I do not know whether there was any other legislation put into effect in Chicago and Washington D.C. that may have influenced the rates, nor do i have time to look them up, but that may be interesting to research before blindly claiming that lifting gun bans lowers gun violence/crime rates, or, even worse, that gun bans promote gun violence/highten crime rates.
"In 1993 a Swiss professor, Martin Killias, published a study of 18 countries concerning gun ownership, homicide and suicide. He in part concluded there was a weak correlation between total homicide and gun ownership."
"Using homicide and suicide data from a larger sample of countries, 35, (International Journal of Epidemiology 1998:27:216), Kleck found "no significant (at the 5% level) association between gun ownership levels and the total homicide rate in the largest sample of nations available to study this topic. (Associations with the total suicide rate were even weaker.)" (Targeting Guns, p 254.)"
"A more recent study, by Killias, concludes "no significant correlations with total suicide or homicide rates were found, leaving open the question of possible substitution effects.""
http://www.guncite.com/gun_control_gcgvintl.html#intl
And about sweden having almost universal guns: in 2007 Sweden was ranked 9th in guns per 100 residents at 31.6 guns which is far from universal compared to America's 88.8 (ranked first in guns per 100 residents, obviously). A country with more guns per 100 residents in Europe is Switzerland (not a part of the EU though), being ranked 3rd in guns per 100 residents at 45.7, and having a higher rate of firearm homicide than Sweden (0.58 per 100,000 in 1994 in Switzerland versus 0.18 in 1993 Sweden, I doubt the 1 year difference makes much of a difference but that remains an assumption) even though it has a slightly smaller population (7.0 million in 1994 in switzerland vs 8.7 million in 1993 in sweden).
http://www.nationmaster.com/graph/cri_gun_own_gun_per_100_res_2007-guns-per-100-residents-2007
http://www.guncite.com/gun_control_gcgvinco.html
A large part of the UK crime rate may be in corrolation with drinking habits or British culture in general, not as much gun laws. Furthermore the UK has a low murder rate compared to the US, even if it is increasing. The UK does have high rates for other crimes and a high overal crime rate, however, but these do not necessarily involve guns.
http://www.telegraph.co.uk/news/uknews/1541699/Britain-tops-European-crime-league.html
Maar doodslaan deed hij niet, want tussen droom en daad,
Staan wetten in de weg en praktische bezwaren,
En ook weemoedigheid, die niemand kan verklaren,
En die des avonds komt, wanneer men slapen gaat.