Since the right to bear arms is specifically predicated on both personal defense and militia service, those should instruct what infringement is permitted, if any. Militia service is for opposing either the US government or a foreign invader, both of which possess tanks and artillery and aircraft. Therefore, private citizens should possess the same by right. However, nuclear weapons would not qualify under this argument, since nuclear escalation would by definition not be winnable. That is the only constitutionally permissible infringement I can see.
Were a citizen so equipped to use such weapons wantonly, local police and sheriff departments would be hopelessly outmatched unless they, too, upgraded--as many are now doing. Another remedy would be for states' National Guard units to be stationed near enough for rapid deployment.