The early waves of mobile communications were largely driven by American and European companies. As the next era of 5G approaches, promising to again transform the way people use the internet, a battle is on to determine whether the U.S. or China will dominate.

Equipment makers and telecom operators in both countries are rushing to test and roll out the next generation of wireless networks, which will be as much as 100 times faster than the current 4G standard. Governments are involved as well—with China making the bigger...