When I think of Europe, I think of a number of different polities. I might think of the union of Aragon and Castile or of Burgundy and France. I would think of the expansion of Prussia with its consumption of other German states and Polish territory. That is to say, I see Europe as being composed of a number of polities (some of which would evolve into nation-states) that engaged with one another, fought one another, and changed over time.
When I think of the Americas I hardly think that. Normally I imagine that there were Mayans, Inca, and Aztec, but I am not really sure what their chronological relationship to each other was. I've heard of other groups (Toltec, who apparently spoke the same/a similar language to the Aztecs, the Teotihuacan, who I thought were Aztec but am apparently wrong, and the Tarascan who I only heard of because I was curious about the Spanish Conquest of Mexico despite them apparently being a major rival of the Aztec), but I know nothing about them. I know that the Aztecs were an empire that extracted tribute, but I have no idea who these tributary states were. I have no idea what was going on in North America at all. And I have no sense of the dynamism that I feel when it comes to Europe.
So what would the Americas have looked like between 1392 and 1592. Who were the great powers? How did they get that way? How did they conflict with each other? How did the different polities respond to the European invasion? For that matter, is there a better time period for this question than from 1392-1592?
(An inspiration for this question was reading on Wikipedia about Proto-Uto-Aztecan. It hit me that I had barely thought Nahuatl was part of a broader language family and that its ancestors might have migrated from present-day United States to present-day Mexico. But, by contrast, I think a lot about the movement of languages and people in Europe.)
This is a complex question to answer, given the sheer number of polities that existed during the timeframe you specified. The common perspective on the history of the Americas is sadly often riddled in stereotypes due to pop history sources, like "Guns Germs and Steels", coming to their conclusions first before providing any evidence. To keep this answer relatively concise, I will be conducting an overview about the polities of the Americas from the 1300s to the 1500s.
First, it is necessary to realize the actual roles European powers like the Spanish played in the Americas. Viewing the history of the Americas a century before and after the arrival of Columbus indirectly hints that the major transformation of the Americas occurred in the year 1492 when that is not necessarily the case for most of the Americas. For example, Cortes conquered Tenochtitlan in 1521, while the Incan Empire collapsed in 1533. Even after these key events, it took the Spanish decades to fully establish control over both the Aztec and Incan Empires after this date, so Spanish control was not a fait acoompli after the Cortes and Pizarro expeditions. The annexation of the Aztecs would not have been possible had the Spanish not had the Tlaxcala as allies. Also, by 1592, the Spanish would still be fighting the Maya for over a century afterwards. So, the Spanish are not this indomitable conqueror but rather a polity that inserted itself into the complex political network of the Americas and gradually asserted more control over the two centuriesin question.
So, as to the actual political landscape in the 15th and 16th centuries, it consisted of a wide array of polities, with significant developments occurring during this timeframe. Along with the Aztecs and the Incas (which may be considered great powers although this term only comes into use starting in the late modern period) there are numerous others including those in the Mississippian culture, such as Cahokia, the Iroquois, who had established a confederacy by the 15th century, and the Puebloan culture. Each of the polities within the aforementioned North American cultures have varied social structures, architecture, food-gathering methods, agriculture, etc. These polities traded and warred with each other. For example, the Aztec Empire started as a triple alliance of the city-states of Tenochtitlan, Texcoco and Tlacopan. The Aztecs warred with the Tarascan empire to the northwest. Also, the Incas in the 15th and 16th century conducted a large scale southern expansion until they were halted by the Mapuche. Thus, like Europe, the Americas also consisted of numerous polities and peoples who interacted with each other in a variety of ways.
As to how they responded to the European powers, as I previously stated, the polities of the Americas responded in a variety of ways based on their geopolitical context. For example, as a subject state of the Aztecs, the Tlaxcalans allied with the Spanish to overthrow them. The Aztecs and Incas fought the Spanish for decades as the expeditions directly targeted both polities. So, there was no unified, single response to the Europeans.
As to a "better" time period, your question is quite Eurocentric in nature by concentrating on the impact of Europeans on the history of the Americas by focusing on the history of the Americas a century before and after 1492. This can result in focusing on certain European-indigenous American relations over inter indigenous American interactions and other European-American interactions. To better understand the history of the Americas without any undue bias, it is best to examine the history of the Americas in its entirety without arbitrary cutoffs.
Edit:
Source: The Earth and Its Peoples: A Global History, Richard W. Bulliet, Pamela Kyle Crossley, Daniel R. Headrick, Steven W. Hirsch, Lyman L. Johnson, David Northup, 6 ed, National Geographic/Cengage Learning.