Can the cervical cancer shot counter the increased risk for cervical cancer from taking birth control pills?

Much more than!: The increased risk of cervical cancer from use of birth control is tiny, if at all, depending on what studies you read. However, the hpv vaccine reduces your risk of cervical cancer by 75-80%, so it is way better! you figure if there is an increased risk of 1-2% from birth control pills, or even it was as much as a 5-10% difference, (which no way it is), then the vaccine really wins out.