The same is not true of Europeans and they generally believe their rights are much stronger than they are. Most Brits are not aware of the true nature of the Investigatory Powers Act. Most Frenchmen are not aware of Article L851-3.
Can you name a single law or privacy practice that Americans have that Europeans don’t?
As for Brits, they left EU and they are definitely going the 1984 way, I think this is generally agreed.
As for the US, 1A doesn't guarantee any form of privacy. 5A does, but in the very narrow sense of not requiring you to incriminate yourself. 4A is indeed about privacy, but it feels like those protections are constantly under fire, and SCOTUS regularly rules against private citizens who believe the government has run roughshod over their 4A protections.
Beyond that, judges seem to rubber-stamp surveillance warrants all the time, and it's currently very legal for law enforcement agencies to purchase private data on citizens from private businesses that have managed to collect it through whatever means. What's the point of the need to get a warrant before tracking someone's movements if the police can just pay Google or T-Mobile for location data? And don't get me started on Flock... they're a government surveillance agency without the "government" part.
Then there's the border search exemption, which is just nuts. Fortunately it seems some federal judges are sane and think the government shouldn't be allowed to trawl through our phones at the airport, but those rulings are not universal across the US at this point. And if and when that sort of case ends up in SCOTUS's lap, I don't trust them to do the right thing.
Frankly I think the US's privacy posture (when it comes to people keeping things private from the government) is pretty bad. Maybe it's still better then Europe, but that's still nothing to celebrate.