The key distinction was not between beheading and hanging, but rather "good" and "bad" beheading and "good" and "bad" hanging. Which in turn depended on the skill of the executioner.

During the Middle Ages, using an axe was a "good" beheading (for its time). That's because it required a skilled executioner to chop off the head with one blow. [Anne Boleyn][1] was executed by swordsman for this reason, and the execution of Mary Queen of Scots, which required two strokes. was considered a "botched" execution. But queens were given the highest consideration for their time.

Contemporaneously, hanging was a "bad" form of execution conducted under what I call the "choke" method. This required (typically) thirty minutes of agony. And it takes less skill for a hangman to tie a rope around someone's neck and throw them off a rampart than it does for an axeman. More on this at the very end. People who don't want the gory details should note the tl;dr.

The Nazis at Nuremburg were executed under the "drop" method, a "good" form of hanging that would knock out the victim immediately and cause death a few minutes later. That is, a victim would be dropped 10-15 feet, depending on his size, so that his neck would be broken. (Japan's General Tojo, a small man, required a drop of only 7 feet 7 inches; things could be calculated that precisely.) Executioners who could calculate such (optimal) drops were highly skilled. This was clearly more humane than the "good" beheading discussed above.

But the Nazis practiced both "bad" beheading and "bad" hanging.

The Nazi use of the [guillotine][2] by the Nazis was a "bad" beheading, even though it was "faster" than the axe beheading. That's because it originated with, and was associated with the French Revolution, to the point where even Hitler was wary of using it. It required less skill on the part of executioner, basically to lift and drop the knife in the slot, and to stuff the victim into the machine, which would do most of the work. Unlike an "axe" beheader, a guillotine was a "weapon of mass destruction."

Back to "bad" hanging. **tl, dr.**

Victims had ropes tied around their necks and were dropped a few feet, enough to "set" the rope, but not enough to break their necks. They were choked to death, typically over a period of about 30 minutes.

The Nazi hangings after the botched attempt Hitler's life were the worst sort of "bad" hanging. People were "strung up" in mid-air with *no* drop. Piano wire was used instead of rope to minimize the grip on the neck. Thus, the "killing" didn't start right away. It took some time for the force of gravity to establish a "choke," and then additional time for the choke to kill. A process that historically took half an hour was prolonged for multiple hours.  




[1]:https://history.stackexchange.com/questions/25674/why-was-the-swordsman-of-calais-chosen-as-anne-boleyns-executioner

[2]:http://www.dailymail.co.uk/news/article-2538973/How-Nazis-slaughtered-16-000-people-guillotine-Found-Munich-cellar-death-machine-reveals-forgotten-horror.html