If you can shoot them equally well, then the larger heavier bullets definitely won't hurt.
But always depends on the projectile, although the 338 is definitely good elk medicine even with plain bullets.
Most bullets made for the 338 are made pretty stout too. I remember reading it in one of the gun rags that this is because bullet manufactures know the 338wm will be used on animals from elk on up, so the pills they use are made with that in mind. Be it thicker jackets etc... According to one of our newer authors here, he wrote this 20 years ago: "If there's a quintessential modern elk cartridge, the .338 Winchester qualifies"... Very true, even by today's standards...