Yes, these two diseases have radically different transmission methods. One is fun, the other not so much.
Yet, would you prefer to catch either of these, or would you rather get a shot and not have to worry about them?
Another false premise (in a list that keeps getting longer) in your argument. Getting the shot does not mean you don't have to worry about getting the disease. Which is why the fine print in the Gardasil ads ALWAYS warns that you still need to get REGULAR screening - the same level of prevention that you would use without taking the "vaccine".