I killed this red stag with a .270 Win and standard factory cup and cores. It was a quartering to shot at about 50 yards and the bullet broke the on shoulder and exited behind the off shoulder. The bull ran about 30 yards and died. I've done the same with elk and the .300 Win.
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The difference in killing power that I have seen between the .270 and .300 Mag with like bullets is minimal at best...I've killed probably 15 critters with the .270 and 20 or so with a .300 Win. YMMV.