From what I've read on many of these internet forums, the .338 Win is THE cartridge to hunt elk with, so it looks like you've made the right choice of rifles.
I've killed a lot of elk, but not with anything that big.
Here's a few quotes that I agree with from other forums:
“The 338 is WAY more than adequate in just about any bullet weight.”
“338 Win in any bullet weight or structure is more than enough firepower for elk.”
“The 338 is a classic elk caliber but is way over the top for most situations. Enjoy your hunt with peace of mind.”