They used different techniques and crops and achieved impressive yields, especially in the Andes, Central Mexico and the Carribean.

Several Native American cultures were ingenious cultivar breeders. It is not a coincidence so many American crops are food staples / "superfoods" nowadays (potato, maize, beans, squash, tomatoes, peppers, quinoa, amaranth, "wild rice", chocolate, vanilla, sweet potato, blueberries, maple syrup, pecan nuts, paw paw, etc). Pretty much all these cultivars were breeded by the Native Americans to be more productive and need less work to grow. No need for a plow to plant tomatoes, or maize. I learned how easy they are to garden this past summer!

They practiced very different intensive cultures, like the Peruvian terraces fields or the North American "three sisters" system. That one was particularly clever: planting maize, squash and beans together made sure each of the plants had what they needed. Beans "injects" nitrogen in the soil that maize needs. Maize serves as the been stalk and the abondant foliage of the squash keep the soil more humid. It's also a great deterrent against pests for some reasons. You also only need a stick to plant the 3 of them since they don't need to be planted very deep, like most cereals.

They knew their shit, if you allow me to be "urban". But their techniques were so alien to the Europeans that they didn't understood their sophistication. It's only recently that we understood why paw paw tree is ubiquitous in the Midwest, or the maple tree in the North East. Native Americans planted them, even breeded them, like the sugar maple. Some species are startling: the reason why you find ragweed everywhere in the US and Canada is that the aborigines planted it. They are less allergic to it and used to eat it before they learned how to plant maize.

As for population density, well, Peru, Mexico, Hispaniola, Colombia, Venezuela were more populated than Spain or England in 1450. Cuzco, Quito, Tenochtitlan, Texcoco and others were urban sprawls larger than London, Rome or Florence and competing with Paris and Cairo in size and population. Even sites like Cahokia or Mesa Verde would have been big cities in Medieval Europe.

One can hardly understand how the European discovery/conquest/colonization of the Americas plus the effect of the Little Ice Age ravaged the Aborigines. Estimates of 90% depopulation between 1492 and 1600 are considered like probable. Entire regions were completely depopulated. I'm thinking of the St-Lawrence valley in Canada who had dozen of 1000+ habitants villages in the 1530s and was completely depopulated before 1600. In that case, the petty kingdoms/polis style states described by explorers collapsed under epidemics, then famine and war.

The Aborigines met by the second wave of European settlers in North America in the 1600s (English, French, Dutch and Scottish) were survivalists remnants of larger former civilisations, exception made of the Iroquois confederation and the Creek Nation, two of the most resilient polities I've ever heard off. But even then, archeology points out to a sharp decline in population in these groups in the 1500s. So, we don't have the whole picture of their agricultural skills since they already lost so much.

As for scientific skills, we know they were no chumps. Mexicans were very good astronomers and mathematicians DESPITE being isolated from the Indian-Persian-Arab-European pool of research and innovation. Incans would have amazed Romans and Chinese with their engineering. A lot was lost in the Spanish conquest because the Inquisition got freaky with the Mexican books and destroyed most of them. The Incans, we don't even know how they taught stuff, but their engineering and architecture ask for good maths.

The Aborigines sucked at metallurgy because they lacked the easy access to copper, tin and lead needed to start the technological ladder. There is evidence the Mexicans and Icans were beginning to smelt (? not sure if its the right term, english is not my 1st language) copper and bronze, but they needed a couple centuries to figure out to make hot enough furnaces

Edit: (my comment was posted by accident before it was complete. 4 yo toddler implicated...) to make charcoal, iron and steel. So no ploughs or iron tools. Even then, they made pretty good without them.