Maybe we could re-frame our thinking with a more familiar analogy: Which is a better hunting cartridge, the.30-06 or the .300 Winchester Magnum? Conventional thinking establishes that, with comparable bullets: a) the .300 hits animals noticeably harder at all ranges; b) inside 350 yards or so, the .30-06 will do anything you ask in style; c) at 500 and beyond the .300 is probably better because it will hit at 500 like a .30-06 hits at 350. The .300 also drops less and drifts less in the wind, so that is an advantage at 500 and beyond, assuming the accuracy of the rifle is up to the task.
However, all of these facts aside, most people will agree that very few shots are made on game in the real world beyond 350 yards. If you are the kind of specialized shooter who plans to do this on a regular basis, then you will: a) have the experience to read wind and make corrections; b) have the time and a good rest to think it through; and c) have a super-accurate rifle with a tuned handload, usually involving a long-range bullet and an appropriate barrel twist, capable of bringing the animal down in short order. In this situation, you've probably got a cartridge selected for its excellence in this rarefied job, and you are prepared to buy whatever you need.
Putting it all together: the .223 (or .30-06) should be excellent to 300 or 350 yards for animals within its class. Beyond that, you need a specialized rifle and skill set, anyway, so choose carefully with a mind to making the most out of your opportunities.