I'm thinking that if a 180gr VLD, a bullet known for fragmentation, hits the ribs at 2030fps at 800 yards, it's gonna shred that animal's lungs. If an animal's lungs and heart look like they lost a knife fight with Freddy Kruger, then that animal is going to die pronto, regardless of the diameter of the bullet that did the damage.
Another variable- what if the 7mm bullet breaks a shoulder on its way to the vitals, while the .338 bullet goes in behind the shoulder and hits nothing but ribs and lungs? I'd say the 7mm is more likely to drop the animal on the spot, in that case.
There are just too many variables to say that the .338 will always have a more pronounced effect. I'm not saying that the .338 can't be more dramatic in how game reacts to the shot, but to say that it is always superior to the 7mm is inaccurate, IME. Is the .338 a bigger gun? Yes. Is the increase in size always directly translated into effectiveness on game? Not always. Again, this is according to my experience. Others' may differ. Impact velocity and bullet integrity/construction are larger determinates in effectiveness on game, than is a slightly larger bullet, assuming that the bullet is large enough to damage a sufficient amount of vital tissue in the wound channel to cause rapid death. A .223 or .243 on elk might be questionable, in this regard, but a 7mm bullet is plenty for elk-sized game, as long as it hits vital tissue and expands properly.
The 195gr Berger EOL with a 0.796 BC should make the 7mm that much better as a LR game getter. Even pushing that bullet at 2850-2900fps from a 7WSM or 7RM would offer a heck of a lot of performance, considering how little it costs in terms of powder consumption, recoil, muzzle blast, etc. And if we're talking about a LW mountain rifle that is elk-capable, those factors mean a lot to me.