Within the confines of the velocity limitations of our current canister grade powders, our current premium bullets, and our current cartridges, the only way to significantly increase power - as it pertains to killing game - is to increase caliber and thereby bullet weight. A .30-378 will never be the equal of a .375 because you cannot shoot 380 grain .30 caliber bullets at .375 velocities - regardless of the cartridge used. The reason that this is important is because fully expanded, a lighter .30 caliber bullet would not have the momentum required to penetrate tissue equal to the .375 bullet nor would it's cross sectional area match that of the .92" fully expanded 380 gr. bullet. If of equal weight, the .30 caliber bullet would be unable to match the velocity of the .375 bullet, which would negatively effect both penetration and bullet upset. Speaking of bullets, even our best premium bullets have a pretty checkered performance record when impact velocities exceed 2700 fps. Therefore arguments of which cartridge is a better killer based solely on which cartridge has the higher velocity may not hold up under close observation. And so it goes, a .308 is not a .375, a .375 is not a .458, and a .458 is not a .600.
The question was to compare the .300 Winchester to the .300 Weatherby, and as such we can see that given theoretically equal rifles, the Weatherby has an advantage of some 150 fps. Most of us with any shooting experience at all know that such an advertised advantage is dubious at best, simply because rifles are not equal, so in some cases the Weatherby might have an exceptional velocity advantage, but in the next case may not have any advantage at all.