Yeah, the velocity will drop some, but exactly how much can't always be predicted, due to difference in individual barrels. The only way to come up with a real baseline would be to chronograph some .300 H&H ammo in a .300 H&H barrel, then rechamber the same barrel to .300 Weatherby and chronograph some of the same batch of ammo. Even then, however, different .300 H&H ammo would lose different percentages of velocity.
I've never done exactly that experiment, but did fire some Federal .257 Roberts ammo once in a .257 Ackley Improved chamber. I'd shot the Federal ammo in enough Roberts rifles to know it usually got very close to the advertised velocity of around 2800 fps, and in the .257 Ackley rifle it got about 2700.
