you must understand what kills the deer. With Archery, it is blood loss. It is not shock to the CNS, or breaking of large bones, it is blood loss. SO if you place the arrow with a quality broadhead( I recommend atleast 3 razor sharp cutting edges, check you local laws regarding this) through the lungs, you have a dead deer, same with a heart or liver shot.
Of the two I have taken this season, one arrow caught one lung (quartering towards) and went through the liver. I heard the deer go down after he took off like a rocket. There was no exit hole, but he left a good amount of blood at the initial hit spot, broke off half the arrow and took the other half including broadhead with him a mear 40 yds. That was a fair body sized cull buck. Ther doe was shot downward through both lungs at only 10 yds and fell just out of sight of my stand.
How does a bullet kill? I will let someone else answer that, but mostly it does a good (hopefully) amount of damage to internal organs adding a shock to the system etc..etc.. They may react the same, but a complete pass through with an arrow through the lungs should leave a good blood trail. Good luck.
markc