I shot my 1st moose in 1975 with the 300 WBY. I bought a 338 WIN Ruger 77 in 1980...shot a dozen or so moose with it. My Dad and brother-in-law, one of which was always along, both used the 300 WBY. 2 years ago I sold the 338 and pumped the money into a 300 WBY.
Here's my obervations after 29 years of moose hunting:
1) With equal weight guns, the 300 WBY has a sharper kick than the 338's rolling kick.
2) Close up, the 338 is a better choice than the 300 WBY. The additional velocity of the WBY is tough on bullets...even a good bullet will explode when hitting moose & bear close-up. On several moose & bear we'd find a entrance hole and no exit hole...massive destruction...the back-side of the hide gives you the impression that the animal was hit with a shotgun...bullet fragments everywhere. The slower 2700fps 338 bullets seemed to stay intact.
3) Beyond 300 yards, the WBY has more energy than the 338. The 338 drops twice as far as the 300 WBY.
4) The WBY is twice as noisy as the 338. Torch it off at the range & the other shooters will turn and look where the BLAST came from.
5) At the range both loads suck. I'm 6ft 220 Lbs and I find that more than 10 shots from either will leave bruses. In the field you don't notice either one. Hold on tight & don't get too close to the scope...I've had 2 diff friends get scoped when shooting my 338.
Bottom line is both are excellent loads capable of killing anything in north america. If you're shots are all under 200 yards, go 338. If you want the ability to take the occasional 500 yard shot, go 300 WBY. Don't mess with all the new designer loads...they will be short-lived compared to these 2 american classics.