It seems to me that the thing that causes a quick death, is the quckest possible severing of the sources of livelihood. When Rashi DH Misah writes that the sword is applied on the side of the Simanim", the Simanim he is referring to are the "Kaneh" and the "Veshet" - the windpipe and the esophagus. These two pipes are the source of life for a person and when they are cut, death is very quick. In fact, even though the head is later decapitated, nevertheless the person is already dead before this - once the Kaneh and Veshet have been cut. On the other hand if decapitation starts from the back of the neck, death is much slower and probably only occurs when the head is actually cut off, but the life-source still exists until the Kaneh and Veshet have been severed, which takes a lot longer if one starts from the back of the neck.

This is why Tosfos writes that if the heart is pierced, death is also very quick because, again, the heart is one of the body's sources of life and obviously one cannot live at all without a heart, just as one cannot live without a windpipe and esophagus.

(In addition, the Shitah Mekubetzes writes that it is possible that if one starts from the side of the Simanim, the normal way is to use a sword, whereas if one starts from the back of the neck, the normal way is to use a "Kupitz" - a big knife or axe. A sword is much sharper than an axe so this is another reason why being decapitated from the direction of the Simanim is a quicker death.)

Incidentally, this is one of the reasons why Jewish slaughtering of animals is very humane, because the principle is that one must severe both the windpipe and the esophagus (see Mishnah Chulin 27a). This way the life-source of the animal is cut very quickly and the animal dies immediately.

KOL TUV

D. Bloom