Until the French Revolution, when the guillotine was used to execute nearly everyone accused and "convicted" of treason, beheading was usually reserved for nobles. It was a quick and relatively "painless" death IF the executioner knew what he was doing. If not, one can only imagine what kind of agony the headsman's sword could produce.
What happens when the head is severed from the body? According to commentary by Mexico's Consejo Nacional para la Cultura y las Artes, a head that is cut with a swift, clean slash is fully aware of its fate for the first few seconds. Not a pleasant thought, is it?
If beheading was the preferred method of torture for nobles in the Middle Ages, death by burning at the stake was the preferred method for heretics accused (and convicted) by the Inquisition.