This is a very tough question to get n proper answer for because it is very subjective; after all, what do you mean by greatest?
If you are asking is it the greatest from a sentimental standpoint then most U.S. citizens are going to say yes while most non U.S. citizens are going to say no (presumably because they are going to feel their own country is the "greatest")
Beyond the sentimental side of the question it is still difficult because there are so many potential factors that have to be looked at. Certainly it cannot be argued that the U.S. is the greatest country in the world when it comes to healthcare for example; however, likewise it certainly can be argued that the U.S. is the greatest country militarily. Economically the U.S. could both be argued to be and to not be the greatest country in the world depending on what factors you feel are most important; do you look at GDP, strength of the middle class, trade, etc). There are dozens of different factors you could look at an then dozens of different sub-factors in each one of those that you could consider in trying to answer this question; which of course means at the end of the day there is no real definite answer to this question - simply many different opinions (even those who agree it is or it isn't are going to do so for different reasons).