Pizzaman - If you are not using a brake, just make sure that your .338 has sufficient weight to compensate for the recoil of a .338 WM. If you get your gun too light, it will turn into a beast! And you will not like it!
Some years ago, I purposefully built a lightweight .338 WM on a classic M70 stainless action. Number 4 fluted barrel (Lilja), Rimrock stock. No muzzle brake. Small scope. Wanted it light. With four rounds of ammo, scope, and sling (in other words, field ready), the rifle weighs in at 8 lbs 4 oz.
I like to shoot 250 gr Swift A-Frames in it. Have also used some 250 gr Nosler Partitions. This is not a long range rifle, but was built for hunting black timber elk. It was also used on a couple of Alaska hunts for Sitka blacktailed deer in the midst of the big brown bears.
Anyway, the recoil on this rifle is formidable. Shooting this rifle off the bench is a tough job, and the recoil is really too much. Nonetheless, I have been successfully hunting with this rifle for many years now, and there is no other rifle that I would rather have in my hands in the middle of grizzly country. I have never had to use it on a grizzly, but I have stood with it ready while waiting for Mr. Griz to make his move.
But truly this rifle is too light. So either keep the gun weight up, or else use a muzzle brake to tame the .338. The cartridge is just as good as everyone else has already said on this thread.
And like memtb, my wife hunts with one as well. Hers is an old tang safety Ruger M77, which is just a bit heavier. Makes it a little easier to shoot too.