Winchester does not offer the 338 Federal. Nor do many others. If you want something a little different, and don't mind the fact that ammo is not as easily available then it is not a bad round.
But it won't kill anything a 308 won't kill. And you don't have to worry about the 308 being phased out in a couple of years. 308 and 30-06 ammo is everywhere with a wide selection of loadings suitable for everything in North America from prairie dogs to grizzly. The 308 shoots the same bullet weights to almost the same speeds as the 338 Federal with handloads. The 30-06 shoots the same bullet weights faster, and the extra .03" bullet diameter is about the same as your fingernail. I don't see that making any difference.
It comes down to this. Do you want something a little different, or do you want to be practical? Nothing wrong with either approach and I'm sure the 338 Fed. kills stuff just fine.