Are vegetarians/vegans susceptible to the same health-related diseases as omnivores?

I think vegetarians/vegans are less susceptible to illnesses. A persons diet has a lot of input on one's health. Ever since I became vegetarian I have not gotten a cold and this is coming from a person that would take months to get over a cold. I think when a person has a healthy nutritious diet their immune system is much more equipped to fight off viruses and illnesses.