Quite interesting that Nazis contemplated using electric current to execute prisoners. In a way they did kill quite a few in this way: some concentration camps had electrified fences and sometimes prisoners would commit suicide in despair by throwing themselves on the fence.
As bloody and ghastly as a fallbeil beheading is, execution by electric current is hardly any less revolting. The skin turns brick red, the body temperature rises to about 140 degrees F, and often stench of burning flesh accompanies the execution. This happens even when the execution proceeds smoothly.
Typically, a self contained generator is used to generate the required current, so the old myth about electric lights in the building dimming while somebody is being electrocuted is just that - a myth. About 2000 Volt potential is necessary to induce the current flow of about 10 amps through the body - this corresponds to skin resistance being as low as 200 ohms. Skin resistance varies from several hundred ohms to many thousands of ohms, so it is imperative to use brine soaked sponges where the electrodes make contact with skin, to lower the skin resistance to as low value as possible.
As little as 0.050 amperes (50mA) of current is enough to cause heart fibrillation and death. 10 amperes is 200 times the treshold lethal current.
In the US, most electrocutions were followed by a mandatory autopsy, which included sawing through the top of the skull and removal of the brain (e.g. Sing Sing prison electrocutions). So one could say that the condemned were partially beheaded after the electrocution. This was done no doubt to ensure that nobody would survive the electrocution. They were obviously not trying to determine the cause of death.
In a beheading execution there is no need to worry about anybody surviving the execution if the head is removed. . People have survived hangings, shootings, even an electrocution when the chair partially malfunctioned, but nobody has ever survived a complete beheading. Which makes it a fool proof execution method.