They had kept up in the mid-range a few years ago. But this standing is sadly long gone.
If you need a fast Opensource'ed LLMs you can go for EU-hosted DeepSeek or Qwen.
There definitely have been Chinese companies with models that fell behind, which is the more direct comparison.
As for the EU in general, there are not a lot of known options. There are some working on things.
The US, the EU, and China all have frontier labs that have yet to release anything.
What’s the mechanism that could today prevent other companies from using LLM outputs to train their models?
Mind sharing such cases? I'm not aware of any so far. There's the one with images, but that's commonly miss-understood, that case was ruled on a technicality (i.e. copyright needs to be attributed to a person, not a model)
That is not the direction American judges are taking. Right now, they are saying that LLM output cannot be copyrighted. And if looting copyrighted works for training is fair game, I really don’t see how one could argue that learning from other LLMs is not.
Mistral is playing the smart money on vertical products rather than horizontal ones. The former requires finesse, the latter brute strength.