I too hate to take the 300 wby to the range...but I also never notice the recoil in the field.
Buy the 300 wby unless you plan on staying at the range.
My family & I have taken dozens of moose over the last 30 years...half with the 338 win, the rest with the 300 wby. Both loads are excellent...if you hunt close-in (under 300 yards) the I prefer the 338. Beyond 300 yards the 300 wby is my choice...drop at 500 yards is half the 338 (about 20" vs. the 338's 40")...with plenty of energy left for a train-wreck kill. Recoil wise, the 338 may have more ft/lbs in your shoulder, but I don't think it's as sharp a kick as the wby. I prefer the win kick to the smaller wby.
I see you are from BC...I assume you have Griz. I would feel short in the pants with a 7mm & a brown bear...go with the larger loads unless you are primarly deer/elk with few griz.

I have a synthetic Weatherby Vanguard in 300 Weatherby Magnum, I shoot Remington 180 grain Core-Lokt ammo, at $28 a box. I mounted a Zeiss 3X9 Conquest scope on it last week. Its not the nicest gun in the world to shoot, it stings, but I take it a lot better than my 12 guage shotgun shooting the big 3 inch magnum shells. Those things deliver between 50 and 60 ft-lbs of recoil energy.