To me, and to the question, it's all about shot placement (undeniable truth: time and time and time again), using any legal caliber where one lives. And, fast or slow, moving such heavy or light weight bullets out of the firearm used, dead is dead. A bullet through the heart of a critter will kill it quite quickly, making it quite dead, quite quickly. Yeah, and I've heard the age old stories how the deer was heart shot and ran half a mile, depending on the adrenaline... I've personally never experienced that phenomena. But then, there's American Bison stories in the wintertime.
I'll give three usages of different firearms that have worked very well for me on DEER for the past 50+ years of big game hunting, shooting BROADSIDE through the animal:
1.) J. Henry English pattern trade rifle (percussion ignition, 30" barrel), using a .58 caliber patched round ball (280 grns.) using 100 grns. of 2fg black powder: When hit in "The Lights," they don't go far, ever (some just go right down where they stand). Either the ball passes cleanly through the body, or the ball is flattened out on the off side of the hide from the entry of the ball. I've killed deer at 150 yds., cleanly, and quickly using this firearm. I've missed some, too... and a gut shot deer is never a good thing using any firearm (IMO).
2.) Ruger M77, 6mm Remington (.243 similar), using exclusively the Hornady 87 grn. S.P. bullet, and IMR 4350 (and now I have a great load using Varget, too) for propellant. I've shot quite a few deer at 200+ yards with this caliber and bullet, and again, a shot in "The Lights," has never failed me. They either go down where they have stood, or don't go very far from where hit... and a gut shot deer is never a good thing using any firearm (IMO).
(NOTE): sometimes the 87 grn. bullet frags, and sometimes the bullet passes through. Either way, the deer dies quickly when hit properly. I have found that the 6mm Remington I have is a very reliable deer killer. My sons will attest to that, too.
3.) M700 Remington, 30-06 Springfield, 165 grn. Hornady S.P. bullet, and IMR 4350 (and now I have a great Varget load, too) for propellant. I've shot a good number of deer at 150+ yards with this rifle and bullet, and as with the .58 caliber r.b. and the 87 grain .243 bullet from my other two firearms mentioned, the results are completely similar. Only with the 165 grn. bullet out of the '06, I've never recovered a bullet shooting broadside through a deer; always a pass through.
And a gut shot deer is never a good thing using any firearm...
And BTW, a 30-30 with a 150 grn. bullet works equally as well on deer at 150 yds. as anything else when hit properly. placement, placement. placement. Ditto with a 45/70 using black powder and a 405 grain cast bullet (20:1 alloy). The 45/70 with that particular load may be a bit of an overkill usage on deer. That load and bullet always passes through a broadside standing deer, even at 150+ yds.
Fun thread to think about; always good to reminisce on past hunts and results.
Happy 4th tomorrow, and God Bless America.