Inside the US, the biggest concerns similarly come with China, which I consider a bigger risk. For better or worse, if you're inside the US, you're probably better off holding as much of your presence as you can inside the US as EU requirements can actually be more harmful than helpful in terms of compliance. There are also certain protections and resistance you can take to less than formal (judicial warrant) requests. Only because if you hold an online presence in the EU, and are forced to violate EU laws, then you're in trouble on both sides.
I would assume similar in most cases, though the EU confederation is something I'm far less familiar with where national laws and EU laws conflict, etc. I'm more familiar with US state to federal structures.