I"ve had and shot both, more the 300 RUM then the WBY, but none the less, there both very very powerful cartridges and either will kill deer and elk a long long ways away, further then about 95% of people even care to shoot.
I had a rem 700 LSS in 300 RUM and shot it for a little over 2 years, shot the barrel out, put a little over 1200 rounds through it, mainly 200g AB's at 3200fps, and 210g vld's/210g wildcats at 3000fps. I had a few kills on deer and elk, furthest being 760 on a buck and 525 on a spike, 775 on a coyote, all bang flops. The cartridge is over kill in my opinion for 99% of hunting shots inside 500 yards. A standard 300 Win mag will do anything the RUM will out to sane hunting ranges, you'll never notice the difference and I doubt the animal will either. The rifle/cartridge was very accurate. With the factory sporter barrel, I had no problems wacking a 15" gong regularly at 1K. Had many many 4"-6" groups at 800 yards.
Then I had a 300 WBY in a vangaurd. The thing would shoot lights out at 100 yards with 180g nbt's at 3150, and 200g AB's at 3100fps, I"m talking 1/2" groups dang near everytime from a bench at 100 yards. However, when I tested those same loads at 400 yards off a bench, I was getting 6-8" groups. Totally unacceptable IMO. Usually a rifle/load that does 1/2" at 100 has no problem keeping 3/4-1 MOA at 400. I dont know what was up with this vanguard, but it was not a consistent LR shooter. For the kind of hunting I do, this is not acceptable accuracy so it was sold.
IMO, there at there best loaded with a 200g AB at 3100-3200fps. There is no animal that will know the difference. They have more then enough power to kill even elk out to 1K.
If it was me again, I would go with the standard 300 Win mag. It will do everything out to 800 yards the others will, with a lot less kick and expense, and a heckuva lot more barrel life.