> My uneducated guess is that the Europeans lived in much larger communities (in Europe), which is a much better breeding ground for disease

Not a bad guess, but completely wrong. The cities of Mesoamerica or the Andes or the Mississippian culture of North America would have dwarfed most European cities, before they were ravaged by disease.

The best explanation I have seen is that almost all domesticable animals in the New World were exterminated early, and so there wasn't anywhere near the cross-species disease potential in the Americas. Old Worlders had domesticated horses, goats, sheep, pigs, cows, a wide array of fowl, camels, dogs, cats, etc, etc. In the Americas, there were turkeys, ducks, llamas & alpacas, and guinea pigs - and not all of those in any one place.