Iliad wrote:I wonder how much do the 25 people know about the other options

or whether they even read them
Ancient greece had an absoluter amazing culture and influence. It stretched thorughout the known back then world and it's culture, it's myths is something which still shines today.
I don't think China is the greatest firstly because it was secluded from nearly all cultures and when it did come in contact with the Europeans they received a pounding. But china was extremely advanced in science. Who knows what would've happened if China was more expansiositic and what would've happened if China invaded Europe in the medieval times.
Rome is a great civilization yet it just conquered and copied other civilizations too much. But you have to give credit not only to the efficient and organized military but also to the administration and integration of other cultures
While many clearly don't (the guy who thought that Mesopotamia turned into Ancient Greece or something), I do. The competition for America comes mainly from Ancient Greece, the Roman Empire, the Mongol Empire, and Colonial Britain. Greece and Rome deserve it because of their profound effect on modern Western culture and the other two had the military strength to make a relatively small country vast beyond anything that could have been anticipated. America, of course, is primarily a military power. It has contributed some things to Western culture, but compared to Rome and Greece next to nothing.
I ruled out the Mongols because they basically looted and pillaged and murdered all over Asia. Not very great in my opinion. The Greeks were never really unified when not fighting an outside threat, so they don't really count as a country (perhaps a nation). Not to mention that outside of cultural influences they don't have much going for them. Britain, when you think about it, just went out and took over a bunch of places who couldn't come close to matching their level of technology. The size of their empire was impressive, but that alone doesn't make them the greatest country ever.
That left we with America and Rome. That was tough for me, as I find the Roman Empire incredibly fascinating. Their empire stretched over the entire Mediterranean, and even after they fell they were revered by Western culture up until modern times (the Caesar roots as an obvious example, czar, kaiser, etc.). America, on the other hand, defied odds repeatedly, going from a rebellion that needed quashing to a legitimate world power in around 75 years. They are, at the moment, the unquestioned strongest country in the world, and have the capability to attack any corner of the world.
In the end I couldn't make up my mind. So, yes, I went for the "USA! USA!" factor.