The largest lethal target on any animal is the heart and lungs. An arrow or bullet shot through an animals heart and/or lungs will quickly kill that animal. A bullet that also goes through the animals shoulder(s) may put him down quicker because he will loose the use of one or both front legs, but a bullet there will also ruin more edible meat.
Last year was the first year that I hunted with the new .300 Weatherby that I built. In January, some friends and I hunted in West Texas. One of tha animals that I shot was an Aoudad. My guide kept telling me how hard Aoudads were to kill, so when my ram turned broadside at about 100 yds, I put the 168 gr TSX bullet through both of his shoulders. He ran about 30 yds using only his back legs. Then in November I was doing a DIY elk hunt near my home in Montana. Again I was hunting with my new .300 Wby and my 168 gr TSX handloads. When the 5 pt bull that I was stalking stepped broadside into the open about 100 yds from me, I put the bullet into the crease behind his shoulder, about 1/3 up into his body. At the shot, he reared up on his back legs, turned around, took two steps and fell dead. Shoulder shots do not always mean the animal will fall quicker.
I generally prefer to aim at the crease behind the shoulder, about 1/3 up into the animals body. Broadside shots are obviously the best, but if the only shot I have the animal is quartering away, I'll aim for the far shoulder. If the animal is quartering to me, I'll aim just inside his near shoulder.
Head and neck shots can be instantly lethal only if the brain or vertebra is hit, but that target is much smaller than the heart/lung shot. Over the years, I have hunted with several friends who swore they hit an animal in the head or neck and the animal ran away and was lost. I even found a .35 caliber jacketed bullet lodged against a neck vertebra of a whitetail buck that I killed one year. The wound had completely healed and I didn't know the bullet was there until I boned out the buck's neck.