Some posters (such as Montana Man)have pretty well covered it already. The .338 shoots flatter with any bullet weight, and penetrates deeper, though that isn't as obvious with premium bullets. This is the reason Elmer Keith dropped the .35 Whelen way back in the 1930's in favor of the .33's, and why the .338 is a standard cartridge among the world's rifle makers and the .35 Whelen a specialty chambering. Even when Remington introduced it, they sold fewer rifles than they had projected they would. Part of this was no doubt due to the factory loads, but it just isn't as versatile as the .338.
Yes, the .338 kicks a little more, and the .35 Whelen shoots flat enough for moderate ranges. But for an all-around big game cartridge, especially in North America, the .338 works better, because it covers basically the same ground as both the .300 magnums AND the .35 Whelen.
