The person who is prohibited from having guns in any space has less freedom. The freedom of knowing guns aren't allowed isn't a freedom of its own, but a constraint on actions. Constraints provide security to do certain actions, improving their viability (hence why EU people may think it does more harm than good), but they don't increase the pool of legal actions, only reduce it.

Also, EU people would be wrong to assume that their countries are gun free. Focusing only on countries with a general ban, the are still a notable category of people who are allowed to bear arms: some government officials. So the security of "no guns" is already compromised. There also some downstream structural effects on building societies on such constraint. But I'd say this is besides the point.

I'm also not commenting on whether some freedom should be curtailed or not, as that's also besides the point.

In the end, given the laws of USA, its citizens do have more freedom than PRC's, even outside of politics. I've heard, for instance, that PRC's citizens have the "freedom to easy housing", but they don't. They, at best, have an promise of easy housing supply from the CCP. Given that housing supply depends on material conditions, it's not a formal guarantee. On the other hand, expressing the wrong opinion online in mainland China may net you arrest.