The 300 BA will kill stuff. It is a step DOWN from 223 in performance. The better modern 223 bullets will shoot all the way through most deer size game out to 200 ish yards and give good expansion. They will kill deer size game farther.
The 300 BA's problem is finding bullets that will work at the velocities it is shot. The heavier 200 gr bullets don't leave the muzzle with enough velocity to reliably expand. Much less expand at 50-100 yards If you want to trust basically a FMJ on deer that is what you get. The lighter sub 150 gr bullets are designed to expand rapidly for varmint hunting, not big game hunting. This is the major complaint with 223 when used with lightweight varmint bullets.
That leaves the mid weights around 150 gr that are designed to expand at 1800-2000 fps. They are in that zone for 100 yards at most before they slow to the point where you won't get expansion.