I went with the U.S. Of the ones on the list, only Britain and the U.S. had truly global reach. The U.S. poses a significant military threat anywhere in the world, whereas the Mayans and even the Indians (who were within the known world) had little to fear from Rome. The reasons are largely technological, but even so, very few other countries in the modern era have been able to effectively fight wars on the other side of the world. The main reason I chose the U.S. over Britain is that Britain had tremendous naval superiority, but I'm not convinced they were ever the greatest land power in Europe. It seems to me all their successful wars against France were either in the colonies or fought with significant help from allies. You can argue that the USSR might have had on-land military superiority over the U.S. (though I've always felt the power of the Soviet army was exaggerated by American intelligence for political purposes), but that's over now.
All these empires were overextended and lost wars to vastly inferior foes under the right circumstances, e.g., Rome vs the Picts, England vs the Thirteen Colonies, U.S. vs Vietnam. In these kinds of cases, it's not so much an inability to subdue the other country, but an unwillingness to divert the necessary resources to do so.