The US has incredibly strong advantages in fields like the semi-conductor industry, but in transportation, pharmaceuticals and aerospace Europe is quite strong. And when you look at hidden champions and the integration of technology into small and medium sized firms, the US heartland has a big problem.
For the EU, if there is a belief that their tech companies can't out-compete against foreign rivals (Think search engine, social media, cyber sec, etc) and that their data could be used against them in the near future, it may seem intuitive to put privacy checkers to get foreign entities in line with your interests.
The large european companies with a big "stake" in the internet are non-technology based companies like publishers. These publishers hate the internet and they hate Google and Facebook because they see them as competition.
The result is shenanigans like Article 13. Also, the GDPR, with its anti Google and Facebook overtones, has received nearly nothing but applause from these stakeholders. So friction was light when it was pushed through by people who actually cared for the privacy aspects of it.