Artificial Intelligence (AI) has become a disruptive technology, promising to grant a significant economic and strategic advantage to nations that harness its power. China, with its recent push towards AI adoption, is challenging the U.S.'s position as the global leader in this field. Given AI's massive potential, as well as the fierce geopolitical tensions between China and the U.S., several recent policies have been put in place to discourage AI scientists from migrating to, or collaborating with, the other nation. Nevertheless, the extent of talent migration and cross-border collaboration are not fully understood. Here, we analyze a dataset of over 350,000 AI scientists and 5,000,000 AI papers. We find that since 2000, China and the U.S. have led the field in terms of impact, novelty, productivity, and workforce. Most AI scientists who move to China come from the U.S., and most who move to the U.S. come from China, highlighting a notable bidirectional talent migration. Moreover, the vast majority of those moving in either direction have Asian ancestry. Upon moving, those scientists continue to collaborate frequently with those in the origin country. Although the number of collaborations between the two countries has increased since the dawn of the millennium, such collaborations continue to be relatively rare. A matching experiment reveals that the two countries have always been more impactful when collaborating than when each works without the other. These findings suggest that instead of suppressing cross-border migration and collaboration between the two nations, the science could benefit from promoting such activities.