EU based cloud services always could compete before. Now they will compete on the basis of being in the EU instead of being better.
Canada, Brazil, Japan, India, and many other non-EU countries have GDPR-like data protection regulation that would be totally acceptable I think (IANAL).
The core problem is USA specific - either the USA needs to implement serious data protection laws where they can't blanket surveil foreign user's data, or EU businesses will have to move elsewhere.
I wouldn't be surprised if in future, similar local rulings appear in Canada/Brazil/Japan/Indian/the rest of the world for businesses based there too. It might be a difficult few years for US-based cloud providers.