I believe it is prudent and wise to carry something that will work for the biggest thing you are likely to run into. So, for me, I would take the 06. Like the man above noted, what if you run into a really big boar. Do you hold your fire or do you try to take him? If you're like most hunters you'll try to take him. The AR is a great coyote gun but in .22 caliber it isn't a great big game gun.
Back in my native CO I once ran into a guy from out of state that was on a deer and elk hunt. He had tags for both and all he was carrying was a .243 Win. To me that made no sense since there is a lot of difference between a deer and an elk. He was carrying a light deer rifle when he was in an area that held elk which weigh over 600 lbs. In my book that was foolish. But, to each their own.