Imagine a 308 Winchester with a lot of additional knock-down power. The 338 Federal is essentially nothing more than the 308 necked up 0.030", which allows it to shoot 185-grain bullets at the same velocity as 165-grain bullets in the 308. In addition, the greater frontal area of the 0.338-inch-diameter bullets makes for greater shock potential.
My first 338 Federal was an unintended purchase. While still having a scout-style Leupold 2-1/2 power scope in that old Ruger "target gray" tone lying around, I learned that Ruger was discontinuing the short Model 77 Mark II Frontier scout rifle that preceded the later Gunsite version. These were the rifles with the heavier 16-1/2-inch barrel and set up for a forward-mounted scope, but otherwise about the same size as the scabbard-sized 77 Compact. The stainless version of the Frontier was in target gray, so I looked around for one chambered in a large-bore short magnum cartridge. Anything available would do, but there were none to be found. I had waited too long. Then I got a phone call from my main watcher helper, who had located a new-in-box Frontier chambered for the 338 Federal. Close enough; I had him steer me to it. As a fan of the 338-06, this shorter version in a short-barreled rifle ought to work fairly well.
The rifle arrived in a few days, and I mounted the scope. Reasonably attractive package; target gray and all with the gray laminated stock. The balance and handling allowed immediate target acquisition with both eyes open, which is a great feature of scout rifles. I liked it!
A trip to the range, however, resulted in the unexpected. After a quick sighting in at 100 yards, I switched over to 300 yards to get some idea of how much bullet drop to expect in field use. I aimed what I thought was high enough, and was surprised at how much too high the bullet strike was. Bill of Northwest Magnum was the spotter as I kept lowering the sighting point, while the rifle kept raising my level of expectation. As it turned out, we were both amazed as to how flat it shot. The ammunition was factory Federal 185-grain Barnes TSX BT. Obviously, the 16.5" barrel didn't result in nearly as much velocity drop off as I had anticipated; undoubtedly due to the combination of the fairly large bore and the use of faster powder than one would even for a 308.
After that, I figured that a normal-sized rifle would be just that much better, so I got a Sako 85 Synthetic Stainless. Light and a pleasure to carry, enhanced by its Soft Touch grip panels, it's a very nice rifle at a reasonable price. To keep it light, I installed a Leupold Mark 4 MR/T (mid-range tactical) in 1.5-5x20mm (one-inch tube) with that fantastic reticle (see their website). This rifle shoots groups of an inch or better at 100 yards, even with just the 5-power scope setting. And it also shoots amazingly flat considering a pretty stout bullet from a small cartridge case. It holds up very well at 300 yards; much better than the 358 Winchester.
There are now several selections of factory loads for the 338 Federal available, but I'm sticking with Federal's load of the 185-grain Barnes. For economical practice, Federal has a 185-grain American Eagle soft point. Upon my latest search, it appears that the Barnes 185 loading may no longer be available, but there's no stopping someone from loading their own. I don't like much heavier bullets in the cartridge, simply because the 185s track along a very similar route as a 165-grain from a 308. If it was known that the distance would be limited to not much over 200 yards, then a heavier bullet would be quite acceptable. However, I would definitely tend to hold short of 225 grains; there's only so much powder capacity here.
Recoil is very doable, seeming to be about the same as a 30-06 would be in a rifle as light as the Sako. There is no question that this compact cartridge is capable of taking a large variety of game, including elk. Increasing numbers of rifles are being offered for the 338 Federal, despite its seemingly slow start in the marketplace. I give it a solid recommendation, especially as a powerful round for lighter, handier rifles.