The issue was not so much a difference in disease between the New World and the Old, but rather the fact that Old World invaders carried diseases that had a few specific characteristics, the most important being that they tended to hit dense populations in major epidemics, leaving the survivors with antibodies that kept them from contracting the disease in the future. When native peoples came in contact with these diseases, they had no such antibodies. One reason for this is that most major diseases that plagued (literally) Eurasia came from people's proximity to domesticated animals. There were so few domesticated animals in the New World that these diseases had no chance to develop. Another is that the types of dense societies needed to support such diseases had developed far more recently in the New World than in the Old. So when the New and the Old Worlds collided, the exchange of pathogens was decidedly one-sided, and had catastrophic consequences for native Americans.