The second amendment is protected more vigorously than the first amendment.
Justice Breyer writes, in his book Making Our democracy Work, pg 167:
... put in terms of constitutionality, the proportionality question is the following: Does the handgun restriction disproportionately interfere with the values that underlie the Second Amendmment? This question encompasses several subsidiary questions: To what extent does the restriction interfere with the protected interest? To what extent does it further a compelling interest? Are there superior, less restrictive ways to accomplish the statue's important competing interest? The answers to the subsidiary questions help answer the ultimate question: Does the statue disproportionately restrict the value or interest that the Constitution protects? The Court has frequently asked these kinds of questions, sometimes using different language, where similar constitutional conflicts - say between free speech and privacy - are present.