I'm somewhat skeptical of taxpayer funded innovation. Seen a few Horizon grants from the side, as a citizen I'd prefer to not pay for them, but unfortunately can't opt out.
My experience with government funding is that they apply something and won't even try to sell it because selling is hard: you don't want to know that the thing you built is lacking nor that the competition is better. Especially the academic types don't. Yet I'm paying for these guys. Also, by funding the academics they won't even need to go to the job market.. But as I paid for their education I thought I was buying people who create value.
Perhaps the above is rather harsh and it's "not that bad", my subjective experience nevertheless.
Vaswani is an Indian born computer scientist, Shazeer is US, Parmar was born in India, Uszkoreit was born in Germany, Jones was born in the UK, Gomez is British-Canadian, Kaiser is a Polish computer scientist, and Polosukhin is Ukrainian.
Almost all of these people have PhDs and Master degrees. The ROI on academia is vast for society, including European universities. The thing the US does well is capitalize on that education, and sadly also try to steal credit for it as "American exceptionalism." If Europe and other countries learn how to keep their academics and get them working in local industries, America's edge will evaporate overnight.
The wider availability of capital is a bigger deal though. "Attention is all you need" is available to people on other continents to read, but a computer scientist in Europe that understood exactly how big transformers were going to be and why had less chance of funding than a webdev in California with a pitchdeck full of cliches and me-too GPT wrapper for an industry they'd barely touched does today.
To be clear, I don't oppose publicly funded education (nor immigrant academics, though I don't see how this relates?). What I do oppose EU trying to compete with tech giants as if they could - the incentives are not set up right, they won't succeed and the funds will be wasted.
There are a few variables here but at this point in time, private-funded innovation isn't different by much and all things considered, the difference isn't in its favor.