I have hunted whitetails with both of these cartridges, using an AR-15 in TX, and a .30 Carbine Ruger Blackhawk (ok, so it was a handgun, not a rifle). Both perform well as long as I keep things within reason.
From a rifle, I suppose I would rather have a .30 Carbine than a .223rem. As much as I love the AR-15 platform and it pains me to say it, but I'm also a big believer in using "bigger bullets". Given the choice between 55grns and 110grns, I'd prefer 110, and given the choice between 30 and 22cal's, again I'd choose 30cal.
However, that's assuming I'm keeping my shots WELL within 100yrds, closer to 50yrds. I'd honestly give the .223rem a longer max range than the .30carbine, since the .30 carb sheds energy like a prom dress, but inside 50-70yrds, I'd give the .30carb the nod.