The history of these two empires shows how they were able to conquer the different variations of subjects, and by this the Mongols had to conquer slightly more technologically advanced populations than the Aztecs had to. Even with being built on different hemispheres and different time periods, it is very odd how they compared in becoming popular and prosperous empires, until their decline of course. Besides their sad endings, their rise, as always, shows the great human ability to find a way to gain power in any way possible.
From 600-1450, the Aztec and Mongol Empires rose and fell but in their rise to power they both needed merchants to work along with their expansion and also both did not create a central government for conquered lands; but, in contrast, the Mongols conquered lands differently. Throughout these empires in some way, merchants supported the expansion of these great empires. The Aztecs, for example, needed them to gain military intelligence of the lands they visited to later on conquer.
The merchants returning with foreign exotic products, such as gems, animal skins, and tropical bird feathers to give to the ruling elites evidence the information gathered about these soon-to-be-conquered lands. The Aztecs also used the merchants to sell the abundance of tribute given to ruling elites to distant lands. Many of these items included translucent jade, emeralds, tortoise shells, jaguar skins, parrot feathers, seashells, and game animals. In the Mongol Empire, they supported merchants and artisans directly more than the Aztecs by making trade routes safe.
This resulted in the increase in commercial investment and the volume of long-distance trade, but more importantly lands of China and Western Europe were directly connected for the first time. The Mongol and Aztec empires were both affected by merchants because trade had existed throughout each society creating this class of merchants to help only during win-win situations because merchants are just ordinary citizens trying to find that perfect trade to get them rich.
Another similarity between the two empires would be that they did not have a central government for conquered lands or an elaborate bureaucracy. Instead, the Aztecs had local governance and the collection of tribute to the conquered subjects but their army was feared. For example, tribute from 489 territories was still brought to Tenochtitlan creating an enormously, wealthy city even without a central government. Chinggis Khan and the Mongols never established a central government also in their rise, but in place put Mongol overlords to watch over local administrators.
They eventually split the Mongol Empire into fourths with the Khanate of Chagatai, Khanate of the Golden Horde, Khanate of the Great Khan, and the Ilkhanate of Persia. Other evidence of this would be the Mongols assimilated to Persian cultural traditions because the Mongols allowed the Persians to occupy high administrative positions. The answer to why they did not have a central government is probably because the rulers were more of conquerors rather than administrators because of the long time spent on laying foundations for the empire and collecting enough tribute and wealth to actually progress the empire.
One difference could be that the two empires conquered lands differently. For example, since the Mongols started in central Asia they started in the steppe lands and the one major thing in the steppe lands are horses. Since being able to train with the horses militarily, they achieved amazing equestrian skills. Also, since the Mongols created major destruction to those lands who resisted, this caused the lands that were soon-to-be conquered fear the Mongols so great that they surrender when the Mongols show up.
The Aztecs had created obsidian weapons that beat other wooden and stone weapons of the other societies. They also created a triple alliance with Texcoco and Tlacopan which made them even stronger. The Aztec and Mongol empires from 600-1450 showed the differences and similarities of the rise in these two different empires, being that they both had merchants as a component to their great expansion, they both had not included a strong, central government, but they differed being that the Aztecs conquered subjects differently from the Mongols.