I'll assume the .300 Mag you're talking about is the .300 Winchester Magnum since that's what most people think of when you say "300 Mag".

Here's what I can tell you. They're both based on the same parent case, but the .300 Weatherby is longer and therefore has a little more case capacity. The larger case holds more powder which translates into a little more velocity, maybe 100-150 fps for the same bullet weight vs. the Winchester mag. In a .300 Wby you could probably get 3200+ fps with a 180 gr. bullet. In the .300 Win. mag you'd probably max out at 3100 fps with the same bullet. That's too little differenceto matter muchin my opinion.

The .300 Win mag. was designed to be shorter so it would work in standard length rifle actions. The .300 Weatherby is longer and requires a true magnum length action as a result. Shorter actions are generally lighter and stiffer and are prefered by many for those reasons.

Rifles designed to shoot the .300 Wby have a considerable amount of freebore. Freebore is the portion of the rifle bore right in front of the chamber that is not rifled. All rifles have freebore, it's just that Weatherbys have more in order to reduce pressures. Why is this important to reloaders? Well, some reloaders, myself included,like to seat their bullets out longer than standard factory lengths so that they are almost in contact with the rifling in the bore when they are chambered. This is done to enhance accuracy. With the .300 Win. Mag thisis an option.With the .300 Wby it's not because of the excess freebore(unless you've got a rifle with a custom chamber).

I've owned both and personally I like the .300 Win. mag better.