Well, seeing as how you asked, I have a lot of experience with all the above cartridges and I've had a 30 year love affair with the 300 Wby. I found the 300 Win not quite up to all that I needed it for and I played extensively with the 30-404 30 deg wildcat, now known as the 300RUM, but the recoil and blast were significantly more than the Wby or Win. I have used the 300 Wby literally all over the world on all sizes of game and I find it superb. If you like loading you can drive 150 gn TTSX at extreme speeds and you can load 220 Parts that make a 338 look anemic. Don't let anyone tell you it's no better than an '06 because I can tell you from real world experience, that's like saying the swift is no better than the 222, it just isn't true.
I've taken game as small as red duiker and suni and as large as Yukon / Alaska moose and Eland and pretty much everything in between. I've taken game at over 600 mtrs and at 16 mtrs. It is the rifle I grab if I'm just heading out for an afternoon or Africa for 4 weeks, and I wouldn't think twice about unleashing it on a huge bear or lion, with the utmost confidence in the outcome. Hell, given some 200 gn TSX's I would hunt Cape Buffalo with it and not feel the least bit undergunned (of coarse they don't allow this), but that is the kind of confidence I have in the 300 Wby and bullet combos we have today.
I've owned several 338s and was never impressed by this cartridge shot several head of game and was always disappointed in the reaction, just not a great killing cartridge, and was never impressed with the 308 trajectory of the 338.
The 300 RUM is also an outstanding cartridge but not for the uninitiated, the recoil is worse than my 340 Wby, way worse than my .375 H+H and is really only for the seasoned and desensitized shooter, but it IS a devastating killer.
Again for what it's worth, JMHO.