The Europeans had much more hard-core diseases because of a mix of factors (including animal domestication), but the chief one was population density.
European diseases evolved in tandem with the people themselves -- each time something swept through the population and crippled/scarred/killed large numbers of the people, the folks with some level of natural immunity would be favored. The diseases would evolve (at a rapid pace, due to reproducing at enormous scale...), as would the people (very painfully).
People in the Americas were mostly more widely spread out. A nasty variant on a disease that wipes out a village and stops there goes extinct.
There were some cities, trading between areas, etc., but not on a European scale.
(Source: "Guns, Germs and Steel", which went into this all in fascinating detail... though admittedly I read it years ago now).