While correct about the deaths, it isn't gun access per se. The US had those higher comparative rates -prior- to any significant gun control in most of Europe, where gun control is an artifact of the post-WW1 period as fears of Socialism, anarchists, and other minorities led to steadily increasing controls. Despite superficial economic similarities to the usual European comparison nations, the US has always been quite different in terms of actual culture and demographics which result in our higher violence levels. 

For instance, the gangs in the UK weren't big on shooting people even before the first real gun control licensing act there in 1920. A quick look at their historic homicide rate, and the rates of most Euro countries, backs this up. They haven't changed since the mid-19thC for most, with -zero- statistically significant change in trend following -any- of their 20C gun control efforts.

It's sub-cultures of violence, not "guns," where violence centers and we have larger ones.