It seems to me that under what appeared to be their intent, they'd be more open for the banning of handguns (as they are more useful in crime than in warfare)
I could get into the details of why it's nice to have a pistol in CQB, having been a troop who was formally trained and issued handguns as backups. Handguns are useful secondary tools for a soldier, when your primary weapon fails, but nothing remotely as useful as a long gun. For a thief or criminal, on the other hand, your primary platform would be a concealable weapon. A soldier would only rarely need to conceal a weapon, and only doing very specific functions.
In other words, the military uses sidearms because they fulfill a useful niche, in certain cases. For criminals, it's pretty much an essential part of their arsenal. When you're looking for someone to mug, it's hard to sneak around with a rifle without attracting attention.
Anyway, my above statement was pure speculation. I don't know for a fact how the Founding Fathers would feel. I'm just imagining what arguments they may have found persuasive, given their reasoning for the 2nd. That it all, and I certainly could be wrong.
I personally enjoy owning my H&K USP .45. She's a beaut. Still, I'd probably be willing to part with her, if the 2nd Amendment were interpreted to mean protection for military grade arms, like machine guns, assault rifles and no restrictions. I can do just fine defending my house with a Mossberg 590 instead. Or a M240G. ;-)