To my knowledge those privacy and safeguard were there since the beginning, originating in a 1978 french law passed in reaction to a government attempt to create a centralized database of all french citizen. This law created the french CNIL[1] in charge of data protection, the first of its kind but soon to be replicated in other countries.
In 1980 work began on a data protection directive[2] which would pass 15 years later after giving birth to 1981's Convention for the protection of individuals with regard to automatic processing of personal data[3]
At the turn of the 2000's through lobbying of various industries and government (including the french government) reversed direction and managed to pass a data retention directive at the European level. This got challenged at all steps from locals to the highest European Court of Justice which invalidated the directive for being contrary to fundamental human rights.
This didn't happened by chance, it took years of dedication and hard work to get there. And it got the attention of a bunch of very dedicated internet geeks who got themselves into politics to defend the internet and privacy. This gave rise to association of people such as la quadrature du net[4] who has been active at the national level up to the European level.
So now the politicians at the European level have a significant amount of backup from concerned citizens and netizens who provide all technical knowledge and background required to understand the significance of technical piece of legislation.
But a most significant difference with the US is World War 2 took place in Europe. (which kinda gave birth to the EU as to prevent Germany and France going to war again a joined union of coal and steel production deal was made which laid the foundation for the European union[5]. The point is Europe and in particular Germany one of the most influential country in the European Union has first hand experience of what the effect of mass surveillance can be and the importance of privacy. WW2 and nazism industrial attempt at genocide explains why the french were outraged by the government attempt at a centralized database of french citizen identified by social security numbers, and why Germany opposed the data retention directive.
The situation is a bit different in the US, when google or the like publicly oppose a bill they're defending their own interest not the general public. When an individual organize people to successfully oppose a bill, he gets pushed to suicide under government pressure probably using the data the govt agencies have on him as Aaron Schwartz story shows.
There's also the economic standpoint, most of the major internet companies are from the US so it makes sense for the EU to defend their population from those and maybe give an advantage to European companies while on the other hand the US has no foreign market dominant companies to defend from and instead has incentive to protect those companies and further extend their domination.
Different histories, different incentives hence different approaches to privacy.
[1]: https://en.wikipedia.org/wiki/Commission_nationale_de_l%27in...
[2]: https://en.wikipedia.org/wiki/Convention_for_the_protection_...
[3]: https://en.wikipedia.org/wiki/Data_Protection_Directive
[4]: https://www.laquadrature.net/en
[5]: https://en.wikipedia.org/wiki/European_Coal_and_Steel_Commun... and https://en.wikipedia.org/wiki/Schuman_Declaration