About consciousness and decapitation: in normal circumstances, once oxygen(through blood flow) is totally cut off from the brain, a human has approximately five seconds of alert consciousness. After that, the brain quickly slips through varying degrees of consciousness into unconsciousness. This is why, in self defense classes, they teach you to get out of or relieve a choke within five seconds(as quick as possible). Sure, the head will most likely be alive for longer than ~five seconds, maybe even twenty seconds, but not in any meaningful sense as it applies to suffering.
However, when it comes to poor fellows who are beheaded in a fashion like the one in this video, it's different. Assuming that they do not faint from shock, they have a longer span of consciousness from the beginning of the execution until unconsciousness. This is because, as can be seen in this video and others like it, the executioner starts at one side or from the front and takes awhile to finish because of the spinal column and depending on blade sharpness and the strength/technique of the executioner. Thus, it is not an instantaneous total cut off of oxygen and so the victim can be in misery for much longer than approximately five seconds.
Now, the quality of consciousness can be called into the question, once one side has been severed, due to blood loss. However, I would bring up the point that the dump of adrenaline in such a stressing situation could be enough to keep one very much aware of what is happening until the majority of the neck is severed. I just hope it is also enough to override the pain receptors and perhaps distract the mind. Especially in this case, because it took that son-of-a-bitch a long time to even get to the spine.
Kantor, the sound is the aspect(out of many) of this atrocity that disturbs me the most as well. More than the sound of the scream, it's the sound of the blood gurgling as the body tries to continue to breath, tries its hardest just to live. Terrible.