I go on my hunts and know before hand that the heart / lung shot is my preferred shot. A head or neck shot, if done correctly will drop an animal in its tracks, but in the heat of hunt, I've pulled shots and I'd prefer to have a larger target area to work with. I have taken two head on "chest" shots on antelope and dropped them both. Not my favorite shot, but I'm confident with it and will do it again if I have to.
The important thing to do is make a clean, humane shot. Wait for a good shot and pass up bad ones. You owe that to the animal and yourself. Also, I'll be the first to tell you that sooner or later, regardless of the shot and how good it was, you'll hit an animal and won't put it down immediately. As a hunter, you must quickly and humanely finish the animal. If you wound one, go get it. I'll relate a story here.
I was in Wyoming and ran across a gentleman who was out there on a dream mule deer hunt. He told me that late one day, he shot a nice mule deer but didn't drop it. His guide told him the best thing to do was leave it, let it die over night and come back and find it in the morning.
The next morning they went looking for the muley and found it. The muley gets up, runs like hell and as the gentleman told me "had his guts hanging out his side."
Any way, they track this muley and watch it run onto a neighboring ranch and watch as two other hunters shoot it and tag it.
This gentleman was distraught that two other hunters would dare shoot his mule deer out from under him especially since he had saved for years to get a trophy mule deer.
While I can't admit that I wouldn't be upset if someone shot my wounded animal and claimed it as their own, by the same token, this gentleman should have never left this wounded mule deer over night. I think he got what was coming to him, but sadly, the mule deer was the one got screwed in this whole thing. Killing a mule deer is one thing, leaving it to suffer is another.
That's a long post but my point is, take the best, most humane shot you can get. Pass up bad shots and if you wound one (sooner or later you will) finish the job. Don't wait for time to finish it for you.