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The 5.56 NATO and 7.62 NATO are approximately equal in effectiveness against soft targets from about 75 (12.5: barrel) to150 (20" barrel) yards.  Beyond that the 7.62 NATO prevails.

While I prefer the 308 as a battle rifle or DMR cartridge, I've field dressed several whitetail shot and killed by the 223. My young sons are trained on the AR15 using a red dot sight and a 50gr varmint round. I've seen both lungs destroyed (bullet did not exit), near spine hits that incapacitate, and a heart destroyed all at ranges from 30 to 200 yards. Every deer they have hit was killed. Although I must say for ranges beyond 300 yards the performance drop is unacceptable. For a smaller person or for CQB there is no better platform than an AR15 (for us lowly civilians) if one uses the proper ammunition. FMJ is for practice fellas.

For grown men, use a scoped 308 DMR for the better range and ammunition commonality. Yes they are heavy, but suck it up buttercup, hunt with it, practice with it, know it intimately. 

The OP is an excerpt from Fred's guide to becoming a rifleman and was a central part of the foundation of the Project Appleseed (of which I am a senior instructor). We teach traditional American marksmanship and I have a altered course which teaches precision marksmanship if any one is interested check out https://appleseedinfo.org/ or contact me.

And I believe that is the ammo both Boston and Suarez are referring to with the above quotes.  

I don't know of any 5.56 that isn't FMJ (even the 'Green Tip" penetrators are FMJ).  And FMJ is about the only .223 Rem ammo one is going to find in bulk.  Otherwise, bring a wheel-barrow full of FRN's if you want to stack non-FMJ deep.

OR.... start getting the components and rollin' yer own.  

I hear the 62gr SP-BT's are the Bees Knees in that regard.

YMMV

Hornady Frontier carries 5.56 mm rounds in a few hollowpoint variations. It will be spring though before I will be able to try them out. Supposed to be a cold winter up here in Alberta, or at least parts thereof. Still have to sight my Ruger Ranch 5.56's new scope.