The US desperately needs fundamental definitions and protections in regard to privacy, but the fact that it is extremely common for European countries to prosecute illegal speech and associations is a big difference. Americans are trying to defend themselves against the secondary effects of surveillance. Europeans can just jail you for saying magic words, or associating with organizations that have been proscribed.

Also, as of a day or two ago, Europeans can be prosecuted for sharing any RT (Russia Today) content, even in private, regardless of content. These are things that the Bill of Rights makes unthinkable in the US. We can bring assault rifles to anti-government protests; if they're seized we can sue to get them back, and to be compensated for being bothered.

The constitutional documents of European countries and supranational institutions might have been largely cribbed from the US's set, but anything like the Bill of Rights in them is virtually never written as an absolute right. It's stuff like Citizens are guaranteed freedom of expression except in cases where it is necessary to prevent expression to maintain safety or the public order.