I don't think that's a correct comparison. If shit ever did hit the proverbial fan, you can bet that any US military walking around an American city would be constantly worried about getting a lead injection from any Tom, Dick or Harry who's got a firearm.
I don't think the same can be said for the vast majority of European cities (assuming the military gets involved).
And then in many scenarios, that Tom, Dick, or Harry gets returned the favor, except with a tank round or worse. If the military remained organized, or at least large factions of it did, it would considerably outclass the general population in both intelligence and firepower / strike capabilities.
Soldiers would be on edge and vulnerable, sure, just like in the conflicts of the past few decades, but overall the military would retain a significant advantage.
And many in the first world haha