HD,
The physical characteristics are completely different on the two rifles. I use them to accomplish the same goal but in a totally different manner.
The 338 Win mag has a custom English walnut stock. I use it as a fair-weather, no backpacking, elk stalking rifle. I'll use this rifle for my moose hunt this year....with care.
The 340 Wby (Rem action also) has a stainless Lilja barrel and a synthetic stock, longer barrel, higher power scope and is designated as my rough weather, backpack, LR rifle. It's not as pretty but it's quite a tool.
Of course, I'm the kind of guy who thinks everyone should have an excuse to have a new rifle any time he/she wants regardless of NEED.
There you have it.
Zeke