From the perspective of fighting, or perhaps more specifically, to come from depression, to draft into two fronts either nearly half a world away, and face the true first face of modern technology and war fighting, is impressive. I don't think most folks could imagine the horrors and extremes that they faced in fighting that war. But I'm not sure that we use military conquest as the basis of "greatest".
I don't buy as much that we would be speaking German or Japanese had we not been as involved. Instead I buy more the situation that these boys were thrown into others' wars to boost our economy, and when we were the last ones (relatively) standing, our economy then boomed. Total war created the economy that we have enjoyed since. Thomas Friedman's works talking about the quest to access and control energy are good reads related to power struggles and conquests associated with energy.
But with that war, and it's aftermath came nuclear weapons excesses, arms races, meddling in others' governments and processes. Despite seeing the horrors of war, they sent their kids off to more of them. Meanwhile, our cities crumbled, our manufacturing disappeared, massive pollution occurred in many places, and their kids are now the greatest monetary liability in existence.
So the story of the general populations' grit and ability to overcome everything is indeed impressive. The country they created and we enjoyed, at least through the early 1960s was incredible (not saying America is anything but the greatest country on the earth to this day, but a lot of things started changing around that time which have caused a lot of the strife we see through today) and set the basis for what the world strives for today. While these folks who went from nothing to a wonderful life (my grandparents and great aunts and uncles, all of who I had wonderful relationships with in my life, were examples), and gave us much of the world we have today, they did make plenty of mistakes that we will be dealing with for generations to come. I don't consider anyone to be the greatest, personally. All have their flaws.
That doesn't mean that the stories, feats and performance of this generation of folks isn't impressive and to be applauded... and I'm not trying to be disrespectful. I just have a desire to think about both sides of any coin. I'd have a hard time coming up with any other generation that came through so much and accomplished so much. And it's that cross section of the situation before the war, during the war, and the accomplishments achieved after the war, which give them the label. But I think its important to also learn from the warts.