30 Carbine vs 5.56 - Military Cartridge Comparison by Ammo.com

I use 5.56 on Whitetails every year and have yet to fail at bringing them down with 1 shot. Where you shoot the deer is critical to do 1 shot kills. I use a zeroed mil-dot reticle RedDot Scope at 250 meters. My 'Guesstimate' on flanking Whitetails without the scope is 1 meter wide. When oblique view its .5 meters and from front or rear lenght shots its .2 meters.
I use 30 carbine or .308 for Blacktails, Caribou and Elk.
For Moose, Water Buffalo and Bear I have used the .416 in my grandftaher's hand-me-down Rigby made in England in 1913.
One shot kills are all about round placement and zeroed distance.
You can kill a Grizzly with a 5.56 BUT you aren't going to see me stalking him. You can also have the biggest shoulder cannon ever build and miss if you don't know the rifle.
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In a pinch would be the only time I'd use either for hunting.

It depends on what you are hunting. I am no expert, but I would guess that 5.56 would be plenty sufficient for waterfowl (although maybe not as advantageous as the spread provided by birdshot) or hares or rodents.

But for bigger game, I can absolutely agree.

In my mind - and I am a COMPLETE AMATEUR here - it is a "different tools for different jobs" thing.