It's really a question that borders on nonsensical, because you can fire 300 Win Mag ammo, in a 300 Weatherby. If you buy a 300 Weatherby, you basically get a 300 Win Mag and 300 H&H included, free of charge- because it will fire all 3 cartridges just fine.
no different than shooting 38 special out of a 357 magnum handgun, with the shell headspacing on the rim. In the 300 belted mag family, the shell headspaces on the belt, the case just fireforms to the chamber. If the caliber is the same, and the case is long enough to put the bullet tip into the throat lead of the barrel, it will fire out of the gun.
Actually there's a lot of difference. The .300 Winchester and H&H will shoot low and with less velocity than in rifles chambered for those cartridges. It's like shooting reduced powder charges in the .300 Wby. You'd probably be lucky to get 30-06 velocities.
The only reason to shoot .300 H&H rounds in a Weatherby is to fireform cases, the need for which vanished about 1950.
