This question is one of the most frequently ask on SH. The replies are the same each time.
Most folks who reply like what they use from 55-80 grains and many express doubts about the other bullets they have not tried. A few place restrictions on range, follow up time or other things. These restrictions are normally based on things they have not tried.
Most have shot only a few critters with only one or a few different bullets. Some have shot nothing with a .223 and hate it anyway.
I live in the midwest and own and manage a fairly large ranch. I guide 10-20 hunters each year, many shoot several does and a buck. Our deer run large. 200-325# range. All hunters use my rifle. 18" Proof or Douglas barreled AR. I also hunt and at times do some culling on permit on my ranch and others. The numbers of deer killed is fairly high. Ranges run from 25 feet to 600 meters with most being from 100-400 M . Most often use issue Mk 262 ammo. (77 grain SMK) I also use a very similar reload. The results I see are as follows.
Almost without exception I note complete penetration with an exit wound regardless of range.
The more closely the shot is placed to the shoulder on entrance or exit the more quickly the deer goes down.
Average distance travled after shot is less than 30 M.
I see very little if any difference in the kills from larger rifles with well placed shots. With poorly placed shots results MIGHT be slightly less effective with the 5.56. I used a .308 for many years.
Young and inexpirenced shooters seem to place shots much better with the 5.56.
The larger deer seem to go down more quickly than the smaller ones. They provide more resistance to the bullet and sustain more damage it appears.
VERY FEW head or neck shots are taken.
On no occasion have I seen the mythical tumbling bullet effect. Not one time out of many hundreds. I am told it is well established but no one says where it is established. I do not shoot light FMJ bullets so that might be different.
Deer hit in one lung will travel a longer distance. Hitting both lungs and some bone is most effective.
I have never seen unusual bullet action. It is uniform as can be. No blowing up, no failure to expand, and again, no tumbling.
I have used 60 grain, 62 grain and 69 grain bullets with equal success, but to a far lesser extent.
If reloading, Ramshot TAC is as good any any powder I have tried with the 77 grain SMK.