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. More highly regarded people got the more skillful executioners and the "better" forms of execution.

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) 10-20 minutes of agony. And it takes less skill for a hangman to tie a rope around someone's neck and suspend them from a cross bar than an axeman to chop off someone's head with one blow. 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 ["long drop" method,][2] 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 several feet, depending on his size, so that his neck would be broken. (Japan's General Tojo, a small man, required a drop of 7 feet 7 inches; things could be calculated that precisely.) Executioners who could calculate such (optimal) drops were highly skilled. This was probably more humane than the "good" beheading discussed above.

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

The use of the [guillotine][3] 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 somewhat 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" in a way that the axe was not. The White Rose people were regarded as "criminals," but not the worst of the worst, see the next section.

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

Victims had ropes tied to their necks, were dropped a few inches to "set" the rope, and choked to death, typically over a period of about 10-20 minutes.

The Nazi hangings, after the botched attempt on 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 a few minutes was prolonged for multiple hours.  




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

[2]:https://en.wikipedia.org/wiki/Hanging

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