Will it kill a deer, yes. Would I personally use it for deer hunting, no. I'd use at least a 22-250 on deer, and have killed many with a .243 (which my magnum friends consider too small). Now, if I were in the woods, stalking, looking at short ranges, then sure, I'd consider the .223. But, if I were to be hunting fields where I take longer shots, I'll stick with my 30.06, and I do consider that gun overkill on deer. It can tear up a lot of meat like many of the faster cartridges, but I can shoot it accurately out past 300yds in field conditions.
As for the bow argument, a bow works quite differently from a gun. Gun is blunt force trauma, basically knock enough crap out of the way and hopefully you bleed the animal out or take out an organ. With a bow, the mechanics are much simpler and more eloquent. Your average 125gr broadhead will slice every vessel that it touches on its way through a deer. Its objective is to bleed the deer out, maybe puncture the lungs. I've had bow shots that'll kill deer that left heart and lungs intact, I just nailed a large vessel. Lastly, most bow hunters that I've known practice much more with their bows than rifle hunters usually practice with a rifle. When I lived in NY I could hit a 3" circle reliably at 60yds with a bow, but that was shooting 50 arrows a day 5 days a week, right now I probably couldn't do that at 30yds. Proficiency is the bow hunters mantra, because being truly proficient can allow you to reach that extra 10yds to kill the buck of your dreams.