The first thing that needs to be said here is that it is a huge problem to look at the question of gun control based around mass shootings. Public Mass Shootings Rampages are rare events that feel common because they get lots of attention from the media. In truth, family massacres heavily outnumber mass killings of strangers, and all forms of multicide (mass murder, spree killers, serial killers, terrorists) make up only a small proportion of homicides, less then 5%. The vast majority of homicides come from drunked barfights, family squables, domestic abuse cases and business disputes between drug dealers. To determine if the american way is effective we shouldn't only look at mass shootings but per capita homicide rates in general. Among the rich western democracies we've got (as of 2016):
Norway: 0.51 per 100 000
Spain: 0.63
Italy: 0.67
Ireland: 0.80
Australia: 0.94
Sweden: 1.08
Germany: 1.18
UK: 1.20
France: 1.35
Finland: 1.42
Canada: 1.68
USA: 5.35
Source The United Nations Office on Drugs and Crime
https://dataunodc.un.org/crime/intentional-homicide-victimsIn short you are almost six times as likely to be murdered in the USA then you are in Australia. Yes there are other factors besides just the guns but overall the american system is clearly far inferior at preventing homicide then other rich western democracies