All three of the great Mesoamerican civilizations were remarkable in some way, but the achievements of the Classical Maya put the rest to shame for several reasons.
One of their most famous achievments is their calendar system. The Mayans developed a complex calendar that tracked years in 52 year cycles before starting over. A priest in the 3rd century improved the calendar system establishing the Long Count system which cycles after every 5,000 years. These calendars, which were based on astronomical measurements, helped the Maya track time, planting seasons, and ceremonies.
The Maya also incorperated their understanding of astronomy into their buildings by placing them in line with the sun and moon. These stone temples were created using advanced engineering techniques.
The Maya also had a very advanced understanding of art and craft as well. They produced textiles in a rainbow of colors, painted their homes and temples with glittering paints made from minerals, and even invented rubber 3,000 years before Charles Goodyear.
To me, It's the Aztec who were a bit superior in this category, but not all superior. Now I'm not saying that the Maya or Inca are lame (Because the Maya made a lot for themselves with science and invention and the Inca had the largest empire of all and lived on Mountains, FREAKEN MOUNTAINS, MAN!) but the Aztecs, even to their fall, were a force to be reckoned with.
The Aztecs, coming from the Northern are of Mexico, came down to rebuild and start a new home for themselves. But they didn't do this on a solid piece of land, oh no, they did it on a freaken swamp island! With superior engineering skills, they were able to create a gigantic city and in 1325, the Aztec capital of Tenochtitlán was created. But why in the world would they build it there?!
Well, According to legend, the Mexica were one of seven Chichimeca tribes who came to Tenochtitlán from their fabled city of origin, Aztlan. They came because of an omen: the Chichimec god Huitzilopochtli, who took the form of an eagle, was seen perched on a cactus eating a snake. The leaders of the Mexica interpreted this as a sign to move their population to an unpleasant, miry, buggy, mess; and eventually their military prowess and political abilities turned that mess into the central agency of conquest, the Mexica snake swallowing most of Mesoamerica. Now that's determination!