You're going to get a lot of opinions on this one, but here's mine:
You've got to ask yourself a couple of questions first:
What's the biggest gun you're used to handling, and how do you feel about recoil?
Ballistically, the 300 Win. Mag. is a great performer, but I've noticed 2 drawbacks:
1)It kicks...hard. It hurts to shoot it at the range. This can have very bad effects on accuracy due to the shooter flinching in anticipation of the recoil. This can be tamed considerably with a muzzlebrake. However, a muzzlebrake is considerably harsher on the ears. Another option is an upgrade in recoil pads (like a Simms for exaple) can make a very noticeable difference. Combining both can do a lot for making the gun more comfortable to shoot...recoil wise
2)Cheap bullets make a mess. The big .30 cal cartridges may put the same hole as the slower .308 and 30-06 on paper, but they DO NOT put the same hole through an animal!! Cheap bullets traveling at the velocities of the magnum cartridges end up making a mess...kinda like varmint hunting. Have you ever seen what hot varmint rounds do to varmints? When hunting big game with a .30 cal magnum, I highly recommend selecting good bullets that will stay together well...good weight retention.
Now, the other thing is ammo selection, availability, and price. The .300 Win. Mag. is much easier to get ammo for than the .300 WSM, or the .300 Rem. Ultra Mag. For this reason alone, I'd favor it over the other 2. However, I must say I was very impressed with the performance of my brother's .300 WSM when I played with it at the range (all it had was a recoil pad upgrade).
My personal rifle of choice, for what I hunt in NM, is the 7mm Rem. Mag. It doesn't kill me on the rest, is easy to get ammo for, and performs well for what I need of it. My particular rifle has taken bighorn, elk, oryx, mule deer, and whitetail deer.
Of all the critters taken by my 7mm, the toughest to put down were the oryx...hands down. I've taken 2 36" bulls, and my nuddy has teken a 39" bull with it...all 3 required follow up shots. Shot placement is very important on any animal, and the vitals on a broadside shot with an oryx is through the shoulder (their vitals are forward and low). However, I think these critters just have a will to live that is unlike our native animals. I know some people have dropped them with 1 shot kills, but I've never seen it. Also, these things will agressively turn on you when cornered, so you want to make sure they go down and stay down.
Hope my opinion helps somewhat.