I hear and get your point, but think that is a different situation. It's a law enacted that is directly related to the activity of voting, and enacted for the purpose of ensuring that someone's constitutionally protected right to "free speech" doesn't intimidate someone taking advantage of their constitutional right to vote. Free speech is one thing, but I think that the ability to regulate and take action on campaigning inside a polling place is a bit like being able to take action against someone falsely shouting, "fire" in a theater....as I understand the law, you don't have the legal right to free speech that would be known to be false and dangerous - which for the shouting "fire" was established by Schenck v. United States (Supreme Court, 1919). As I understand it, all those rights are no more or no less absolute than any other. So that seems to protect the right to bear arms as long as it doesn't interfere with the right to vote. But speech can and has been limited when it has been found to infringe upon other constitutional rights (such as speech that causes intimidation which then infringes upon the right to vote).
Having said that, perhaps I could also make the argument that some folks would claim that "man with gun" would intimidate, but I think that would then be addressed by other laws (that determine that man with gun isn't equal to brandishing, and therefore not an illegal act or not intimidating by itself).
But IMHO that's the difference.