With a vaccine, you get a standardised dosis of an agent resembling the disease or just a part of it. The remaining variability is the response to that standard

With a vaccine, you get a standardised dosis of an agent resembling the disease or just a part of it. The remaining variability is the response to that standardised input. With an infection, you have no control over the degree of exposure, so on top of the variability of the response comes the variability of the exposure. Additionally, in case of exposure of the full pathogen, there is some variability to what part of the pathogen the immune system will respond. That part can actually be a good thing in total.