I'm gonna put down the .308 and 30-06 this year and hunt strictly ar15. If I can't shoot sub moa and feel good about the head shot I don't pull the trigger. I used to hunt with a .221 fireball. It was a deer slayer but I was a decent shot with that gun and I don't shoot further than 150-200 yards.
Those are very light bullets, 55 Gr will drift 1" + in 4 mph wind, small things you dont see (twigs) will bust most fast moving .22 family rounds before the target is found.
Good luck: