Here's where I come down.
ARMS, as defined at the time The Constitution was written, were regarded as weapons intended to be used BY individuals AGAINST individuals. Meaning, muskets, pistols, swords knives etc were arms. LARGER weapons, such as CANNON, were considered ORDNANCE for the purposes of procurement and supply. This worked pretty much until the turn of the 20th century. Machine guns were CREW SERVED weapons, because they were designed to have more than one person operate them, and were effective against elements LARGER than individual soldiers. They were therefore ordnance, rather than arms.
But at the turn of the century, newer developments emerged, particularly in WWI with the Thompson and the BAR. These were weapons designed to be used by individuals rather than being crew-served. We still have crew-served machine guns, but there are also certainly automatic weapons designed to be used by individuals against individuals. THESE are certainly ARMS, not ordnance.
SO, when antis ask me, "So, you think that people should be allowed to have nuclear bombs, right?" I reply, "Nonsense. These are not arms. They are ORDNANCE."
This philosophy isn't perfect, and technology emerges faster than gun laws are changed, but it's a distinction I am willing to live with.