It's an interesting cartridge, but realistically doesn't really offer much that the .308 doesn't already offer. It has more recoil, develops slightly more energy, because it's slightly more efficient. You need heavier projectiles to get the same BC and SD that you would from a .308 bullet, and where the .338 has the real advantage over .30 cal is the heaviest for caliber bullets like the .338 300 grain VLD bullets, which don't work too well in the .338 federal, because it can't really push those projectiles fast enough to have any real long range advantage. .338 Federal should have slightly more barrel life because it's slightly less 'overbore' than .308 win. That's about it.
I've thought about getting a .338 federal semi auto, but every time I want to I just think how much cheaper and more available .308 win is and how the .338 wont really give me anything that the .308 can't do well. Plus more recoil with the .338
I just can't convince myself there's any real advantage or reason for the .338 fed, other than just to have it.