Of these, I would have to argue that the Mayans were the most advanced civilization. The major reason for this is the fact of how long the various civilizations lasted.
The Mayan civilization lasted for thousands of years. This makes it much more long-lived than either of the other civilizations, particularly that of the Aztecs who lasted only a century or so in real power. If we consider that the longevity of a civilization reflects its level of advancement, we must conclude that the Mayans were more advanced than either of the others. Since the three civilizations had roughly the same levels of technology and since all were able to build truly impressive structures, I would argue that the most advanced has to be the one that lasted the longest.