I guess that really depends on what you consider a "1-1 military battle." Gentlemanly warfare used to be people marching and staying in formation and going straight at each other until they died. With that battle strategy, the victor is generally going to be the one with more people covering more ground.
But that strategy hasn't been used in a long while, because there are smarter ways to fight. Tanks and so on are the old way of fighting battle. The US has a decidedly bad post-WW2 record since nobody is really fighting by the "old ways" that much of the American military fights by, and the biggest advantage is the US can just drop bombs indiscriminately basically forever (decidedly not 1-1 combat) and hope to destroy every living thing imaginable (which still failed in basically everything from Vietnam onwards).
The claim that the US will beat any country isn't backed by any evidence. At all. There are theoretical situations where maybe the US has more people, more money, more whatever and will win if you line soldiers up and have them fight Napoleonic style, but in reality, successful wars following WW2 include... the Gulf War? Which just ended up leaving Saddam in power, ending up with the unmanageable chaotic wars we've had in the middle east these past 2 decades.