Just to clarify, the .300 Weatherby is not too much gun in terms of damage to meat. It'll kill deer very well, it works very well for long-range shots, and it won't cause excessive damage to the meat. I have a friend who uses a .300 Rem Ultra-Mag for deer hunting, and he does very well with it. But he's been shooting (and hunting) most of his life, he's as big as a horse, and he reloads. He doesn't mind the recoil from that gun. He shoots enough to be able to use the gun for long-range shots. Simply put, he's a better shot than I am.
Most people (myself included) are not going to shoot at a deer that is more than 200 or 250 yards away, because most people will miss (or, worse, wound) at such long ranges. And personally, I don't like heavy recoil (or heavy guns, for that matter). Heavy recoil leads to flinching. Flinching means you're going to miss.
I can take the .308 to the range and shoot 20 or 30 shots through it before I start to react to recoil. I wouldn't be able to do that with a .300 Weatherby gun; in fact, I couldn't afford to do that with the .300 Weatherby
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And the .308 (and the .270 & the '06) will kill deer just fine out to 2 or 3 hundred yards (although most shots are 150 yards or less), with less muzzle blast and less recoil than a magnum caliber. JMHO.