Although in the interests of full disclosure I don't shoot a 7mm, I do shoot both the .300 Win and .300 Wby. As many here have already stated, there's little difference between the two until you head to the cash register with your box of ammunition. I have found that the Weatherby handles heavier (and generally higher BC) bullets better, but unless you're reloading, you're likely not going to see that advantage and I can't promise that the 7mm Weatherby also possesses that characteristic.

The 7mm Remington Magnum is tried-and-true. It's one of the chamberings I seem to see stocked on the shelves even today. If it were me, I'd probably lean toward the Remington.