There was a Kettner gunshop right in the heart of downtown Vienna when I was last there in 2004. Kettner is a German company, and the largest gun vendor in Europe.
The primary gunbuilding location in Austria is in the town of Ferlach, where some of the finest high-end guns in the world are crafted.
Incidentally, my reason for being in Vienna was to meet a European guide friend who was going to drive us to Hungary, where I was to hunt Roe deer. I already had gun permits for Hungary.
As I landed in Vienna and headed to collect my luggage, I realized that I had forgotten I was going to drive across the country, but had not thought of getting Austrian gun permits. I was temporarily almost in a panic. Before approaching Customs, , I went to the Police station in the airport to tell my story, and there I got the good news: "Mr. O'Neill, that's no problem. A visitor can enter Austria with up to 3 guns with no paperwork. We like guns and hunting here...."
You can't do that in the U.S.! In general, though, everyon's comments above about gun ownership being more restricted in Europe are accurate.