I shot a 110 class buck yesterday morning with my Colt M4 using the same bullet as Krochus (55gr Sierra GameKing). When I shot him, he looked at me and mouthed what I think was, "Silly man, that wasn't a 300RUM." Then he fell over and died.
Ok, not really, but he died quite quickly when that 55gr tore through his shoulder, heart, and lungs. Truth is, if the bullet can reach the heart, it will kill the animal.
Around here, where we reportedly have the highest concentration of deer in the nation people hunt with all kinds of wonder mags. But they are not from here. The preferred deer calibers with those I know who hunt a lot are .222, 22-250, 25-06, and .308. And that's in order of popularity. I even know of one guy who hunts with a 22 hornet. They will kill if you do your part.
Also, I don't know if I would classify the whitetail as "big" game. Seems to me it's a medium game animal.