Ah, this old debate.
Frankly, I think that it was the United States' entry into the war that brought down the Central Powers. Germany still had a lot of fight left in it, had just annexed a huge amount of Imperial Russia, and had bled France to the point where its Army could no longer go on the offensive. Britian, alone, had little chance of defeating Germany. It was the United States, which, by 1918, was the undisputed global power (even if Europe refused to recognise this) that brought Germany to the peace table.
Greatest Army in the world? Hmm... I'll go with the Swiss.