Lloyd's post is all over the map, and because the topic has kind of widened into more calibers than the original 2 {'06 & 7 RemMag} the map has kind of gotten bigger, and I agree with Lloyd for the most part. A proper post on the current topic needs to be all over the map.
Where to start so as to not make the map even bigger...
I think Lloyd nails it when he adds a hundred yards on to 200. One needs only take the relationship of two of my favorite calibers, the 6.5x55 and .264 as an example. If a fellow lives where shots past 200 are common, the obvious nod goes to the .264. It adds about roughly 75 to 100 yards of useful range to the 6.5x55. Especially where the hunter is fighting a bit of wind. It can be seen readily on the targets, whether paper or flesh.
Reason I said what I said earlier about SHOOTING from field positions is that most fellows I see at the ranges can't make use of the extra 100 yards that the magnums provide. Period. {...and BTW, the 7 Rem is not much of a "magnum" when compared to the .30-06}.
As for shooters, what I see is that they might be OK on the bench, but take the support away, and they are a lost ball in the high weeds. Thus, a .308 might kill quicker than a .300 Mag simply because tho Mr Average Hunter doesn't admit it, he buttshoots deer with the .300 due to having his eyes jammed shot when he yanks the trigger and he more occaisionally has his eyes squinting slightly open when he centermasses deer with the easier-kicking and yelling .308.
We watch this each year when we shoot the test I require on the ranch here, the norsk reinsdyrblinker prøve, the Norwegian government hunting shooting test. Fun to listen to the smack, then also fun to watch the bullets fly wide in the ditch...
Anyway, IMO, most hunters should stick to rifle-supporting box blinds, bait stations and 50 yard deer and make damn sure they have a good blood tracking dog asleep in the box with them for the necessary followup to come if they are lucky enough to buttshoot the deer. Fellas, most hunters cannot shoot worth a Clinton promise. There, I said it...
As for trauma, there is obviously more done by a high speed .30 cal cartridge than a slow .30 on deer. "On deer" that is pure advantage, on elk, well, not necessarily if high speed shortens penetration. A .308 is not a .300 and trauma proves it. Using same bullets, the .300 adds that hundred yards and inside the shorter distance wrecks more muscle and bone on a deer and in case anyone is confused, that means the deer runs less after being hit.
When you mix critter sizes as the OP noted, the issue gets a little more complicated.
I've killed elk with the 6.5x55, .264 Win Mag, 7x57, 9.3x57, .375 H&H Mag, my son with .30-06 and 7x57, my friends w/, well, you name it. The very round that gets a fast drop on deer can sometimes cause trouble on elk and that is simply because elk are bigger and the bullet has to go farther inside to cause The End than it does on a deer. That is not a complicated concept.
No one will tell me that there is any difference between the best .30-06 loads and the best 7mm Rem Mag loads on the full range of game the OP cited. None. But to limit himself to deer, well, maybe I might fidget a bit and imply the fastest 7 Mag loads might drop a deer faster on occaision than does the '06. I definitely agree with Lloyd that this can be demonstrated with a .308 and a .300. .300 wins if the shooter does his part, i.e., if the shooter does his part.
But after a different brand of beer I might disagree with myself if the Hunter told me his 7mm Rem Mag was a shaky M77 2.5 MOA rifle and his shots lingered out there at the 250-300 yard range, give or take, and he can shoot well enough to make his Remington 700 1 MOA '06 work for him. Go '06 in that case.
But add elk and well, we are for some reason a little hard on the 7mm Rem Mag. My Father-in-law used one to good advantage, but for some reason others locally hate it, for no ballistic reason other than that they didn't kill their elk with it. As a bore-hole and powder bottle, it is not a bad killer.
.30-06 or 7mm Rem Mag Both on deer? Pick the one you shoot best. If the argument was between a .300 Savage and a .300 Win Mag, I'd say learn to shoot the .300 Mag.
Example; Last Year for sonny and me.
Long Range Elk Country;
Then came the short range {120 and 50 yards} elk. Oh, well, the .264 & '06 were fine anyhow...