The U.S. has the best universities, the most innovative private sector, and the biggest lead on the most important technologies at the moment. And while China may soon be the world's largest economy, truly groundbreaking AI is likely to come from combining the insights from many disparate fields and making them work together — something Beijing will struggle with.
It also matters a great deal who will ultimately control that AI technology. If it's private companies — as I expect it will be — it's far from clear that any government would be able to effectively regulate it. And the more advanced the technology, the bigger the gap with effective regulation. All you have to do is look at the impact social media (and specifically Facebook and Twitter) have had on U.S. politics to begin to understand the scope of the challenge.
As for the also-rans, context matters: You'll want to be economically aligned with whichever country experiences the first true breakthrough. There's big downside for those left out of the economic benefits that come along with strong AI. Of course, this all assumes that things like "states" exist at that point.
Bottom line: Technically, the U.S. wins, and other countries will want to align with Americans so as not to end up on the wrong side of AI. But that won't necessarily be a geopolitical win, especially if technology continues to tear at U.S. governability.
Other voices in the conversation: