That’s quite an involved question, and there could be many answers. Furthermore, it actually contains two questions. Number 1 is why were cities in the Americas generally smaller than in Europe? The second is why was the population densities of the Americas lower than in Europe? These questions are related, but need a bit of a different approach.

To answer the first question, I’d first like to point out that really big cities, even in Europe, were really rare. Before the Industrial revolution only a handful of cities ever cracked the 1 mill mark, remembering of course, that estimating population levels for pre-modern cities is always going to be difficult. Cities like Rome were an unusual exception. Additionally, there were only ever a few of these mega-cities active at one time in the entire world, and they didn’t usually last at that peak for all that long. If we eliminate these outliers, then the difference is less marked, depending on exactly which part of the Americas we are looking at. Since you mentioned Tenochtitlan, Mesoamerica may be a good comparison. If we look at the Classic period (200-900 AD) we see a huge number of cities of large size, including Teotihuacan (125,000), Caracol (100,000+), Tikal (80,000), and Calakmul (50,000). Given that Mesoamerican is a much smaller region than the entire Americas, we can perhaps make a better connection to Europe. Depending on which exact date we choose, Rome’s population had crashed by this point, while we still have the outlier of Constantinople, which I think was around 400,000 at this point. If we go later to the Postclassic period and look at Tenochtitlan we can see something different. Tenochtitlan was probably bigger than any European city (except maybe Paris? I’ve read a few different things), and it was backed up by some other, pretty impressive cities.

Nevertheless, even then cities in Mesoamerica appear to be smaller on average. Nor is Mesoamerica typical of the Americas as a whole. So, why? There are several possible explanations, perhaps the best is settlement patterns. In other words, how do people actually live on the land? In general, Mesoamericans preferred to live dispersed over the landscape rather than concentrated in cities. This allowed them to live closer to their fields, and intersperse their settlements with kitchen gardens. The end result is that Mesoamerican cities tended to be smaller, and with lower population densities than their European contemporaries, even if their overall population densities were relatively high. There were also lots of them. The Valley of Mexico, for example, had more than 30 significant cities in addition to Tenochtitlan. Similar cases can be seen in other parts of the Americas as well, including the Andes and the US South-East.

There may also be political reasons for smaller American cities. Although I’m generalising here, most of the people groups in the Americas were relatively small and decentralised. Big states and Empires were the exception. Although city-states can get quite big, most of the mega-cities only really appear at the centre of large Empires. Rome of course being the obvious example. It is telling that the big cities in the Americas, such as Tenochtitlan and Cuzco, also appeared at the centre of large Empires. North America seemed to lack Empires all-together. Without the economic stability and resources brought by an imperial government, cities like Cahokia probably didn’t have the raw materials to really grow beyond that point.

One final point I’d like to bring up is that our understanding of American archaeology is still quite limited, and there could be more cities in the Americas than we realise. A good example of this is Anguamuco, in West Mexico. This was possibly the second largest city in Mesoamerica at the time with a population of over 100,000. Yet, archaeologists didn’t realise this until 2012! There are similar cases from all over the Americas, including the Amazon and the US south-east. There were probably more cities in the Americas, and larger ones, than we currently know.

This brings me to part 2, the overall population density. There are several legitimate reasons why populations in the Americas could be lower than Eurasia. Mainly, these are to do with climate. The Americas has a lot of jungle, desert, and mountain ranges, that put limits on population density. To use a US example, take the Pueblo nations. They had some excellent farming techniques, well developed craft economies, and were skilled builders. Yet, although they built substantial towns, including apartment complexes, they had no cities. Why? Because they lived in a desert, and that put a cap on how dense or large their populations could be. At a certain point, skills and techniques are just not enough to overcome the problem of having no water. Andean cultures were in a similar situation, only with large cities, complex governments, and even more developed economies. Yet, the Peruvian coast was and is, quite arid, and mountains are a real impediment to urban settlements and growing dense populations. Even Mesoamerica has its fair share of mountains and deserts. Europe, by contrast, is relatively blessed. I don’t want to give the impression that Europeans faced no environmental challenges, but I think that it is reasonable to say that the challenges were greater in the Americas.

However, environment is only half the story. The other half, is that populations may not have been that low at all. Many of the most extreme estimates of population density, at least for the US, were based on the idea that all Native American people were essentially hunter-gatherers. This is obviously not true. Most Native American people groups, even within the US, were agriculturalists. But this was largely overlooked by early writers. Even Cahokia was either ignored or explained away. This goes back to my earlier point about limited archaeology of American Indigenous sites and general lack of historical knowledge of Amerindian societies among the public. Just as Anguamuco was overlooked, it is easy to forget that there are thousands of mound sites across the South-east and into other parts of the US, which were also towns and small cities. As a result, the early population estimates were way off. Although newer studies are generally better, they still have to reckon with these earlier figures, and they are slow to be accepted by the general public, which makes it hard to get support for projects to excavate Amerindian sites.

Another contributing problem may be the misunderstanding of agriculture in the Americas, even among historians. Generally, this takes the form of an excessive focus on maize as part of the diet. For example, William T. Sanders estimated that maize made up 80% of the Postclassic Aztec diet. However, I don’t recall any excavation/experiment supporting that estimate. Some results were much lower. IIRC, Maya people from the Belize River Valley only consumed about 50% of their diet as maize. A similar thing happened with the Olmecs. Scholars initially thought maize was responsible for the growth of their civilisation. Turned out the Olmecs had quite flexible diets. This over emphasis on maize means that other forms of agriculture, including silviculture and pisciculture have been overlooked, giving the impression that the various indigenous American agronomic systems were less productive than they really were. To give examples, Maya and Amazonian peoples were excellent tree growers, while Californian and New England Indigenous nations (e.g. Chumash and Wampanoag) were practicing fish farming, as were some Floridian peoples. In addition, many of these crops could be grown/harvested in places were maize agriculture was not viable. Amaranth and Maguey spring to mind. Consequently, the total productivity of the land under cultivation by various people groups in the Americas has almost certainly been underestimated.

To conclude, I don’t really know how populated the Americas were. But that number is likely to be higher than you would expect.

In addition to the really nice breakdown of the problem that u/Tlahuizcalpantecutli gave in their post, you might be interested in this previous answer of mine to a similar question: At the time of Europeans reaching America in the 15th century, were there any cities or settlements which were larger or more populated than the biggest cities in Europe?