I killed my cow last year with a 150 NBT from a 308. 150ish yards and it was a mature cow. The bullet smashed though the onside shoulder and the jacket was under the hide behind the opposite shoulder. Couldn't find the core, but the jacket penetrated the meat between the ribs.

The cow stumbled 30 yards or so and dropped....

The 165's you mention in the '06 should be just fine..

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I enjoy handguns and I really like shotguns,...but I love rifles!