The Weatherby is 100-150fps faster. I have a couple 30-8mm Rem. Mag's (basically the same as a .300 Weatherby) and they run 3100fps with 210's where most .300wm's run 2950-2975fps. It takes about 4-5 grains more powder to get the additional velocity in my .30-8mm's. The Weatherby will be a bit more with the excessive freebore. The .300 Norma, .300RUM, and .30-378 are even faster if recoil and price aren't a issue.
I am going to stick to the OP's paramiters....I LOVE the 300 WBY. I have done the load wokup on quite a few WM's and WBY's, so I feel that I am qualified enough to dicuss it. I like to shoot the berger 230, so the WBYs extra boiler room is a big help. I have been shooting WBY's in 1000 yard competition, and have done LOTS of tinkering with it over the years. my findings.....go strait to RL 25. I have MANY WBY tubes and they ALL love RL 25.
I am not saying that the Akleys, Normas, Lapuas, ect arn't great rounds....just keeping with the OP.
The 300 Weatherby is simply a blown out 300H&H case. lt was thought up by wildcatter Roy Weatherby. lt takes a special long magnum action. The 300 Winchester Magnum is shorter and fits in a standard 30-06 action. Granted, you get a tiny bit more speed with Ole Roy's wildcat. The 300 Winchester beats Roy's 300 six ways to Sunday in the ACCURACY department. Accuracy is to quality as speed is to quantity. l choose quality over quantity ANY DAY
not sure you know what you're talking about, seems to be generic bs you're parroting that you read somewhere, rather than actual, physical experience with both cartridges along with multiple others as a direct comparison, 30 caliber has been my world for 30 plus years and I can assure you the 300 Wby is capable of same accuracy as the 300 Win Mag, same with the 30-378 Wby