Would the advantage not be distance and stoping power over the .308? because the .308 tops out about 2700fps while the .300 win mag is about 3300fps (yes you can fully load your case and get a little more velocity or lower the grain of the bullet and thus increasing velocity). As well for the recoil im not planning on shooting more than once while im hunting anyways right? so why would i need to use a muzzle brake (il just deal with the recoil when i need to) now when i go to the range to digi in my range cheat sheet il use the muzzle brake so i can shoot longer. So really the reason for it is better accuracy at longer distances and of course stoping power compared to the .308. Hell even the U.S.M.C is going to be switching there .308 to the .300 Win Mags.
As well there is a reason for it being one of the best selling calibers on the market still to this day. Actually its doing better now than it ever has.
But i know you .308 guys are die hard for your calibers and dont like to keep an open mind to others