Don't frame this as a free speech issue. Freedom of speech is as protected in the EU as it is in the US, possibly more.
Freedom of speech in Europe is not just an EU question, but also - and mainly - up to constitutions and legislation of the member states. So of course it varies. But there is less surveillance in Europe on what citizens say online, European media is less centralized than American, there are more parties with opposing views in parliaments, much less political correctness in both politics, business life, and social life. Most importantly, European courts is most member states uphold the protection of the individuals' freedom of speech.
This is legislation aimed at Google and Facebook, and other large companies, yes. Go back 15-20 years, and nobody would have thought that Google would get away with using the creations of content providers without paying a fair share. I don't see anything wrong in Google or Facebook being forced to apply filters. We have gotten used to what is truly an disgusting situation where creators of music, journalism etc. don't get paid and their works are put out on Youtube, Facebook etc. I would have liked to see a higher threshold so that only truly large companies had to worry about filters, but again; these filters will likely be easy to find in 10 different versions for free on GitHub in a couple of years, and better ones you can license for a small fee.
But I agree, Europe should finally start to tax Facebook, Google, Amazon etc.