Population estimates for the Pre-Columbian Americas are notoriously difficult to pin down. The current high-end estimates put the population in the neighborhood of Europe's at the same time, around 100 million, give or take ten million (Europe's population in 1500 was between 90-100 million). Conservative low-end estimates place the population at around 50 million instead. Either way, around 50% or more of that population would have been concentrated in Mesoamerica and the Andes.

So it's possible that the population of the Americas was greater than of Europe in 1492, but that requires the highest estimates to be accurate. I tend to fall in line with the High Counters on this issue, but I'd be hard-pressed to say that the American population was higher than the European population at the time until we have more concrete information, rather than statistically equivalent, given the margins of error involved.

A bit stereotypically for /r/AskHistorians, I'll recommend 1491 by Charles Mann. It has a good summary of the shift from the old estimates of merely 10 million toward higher estimates of 50-100 million. If you don't have time for a whole book, this older article summarizes the basics. Sad to say nothing has radically shifted the debate in the last twenty years here.