Depending on how strict you are with your military lineage there may be very few options.
Anything based on an ‘06- 25-06, 6.5-06,.270, 280, 280AI, and more
Anything based on a 308- .243Win, 260Rem, 7-08, 338Fed, probably more
6BR wouldn’t even count if you were being picky. It was based on the .308x1.5” which was just a shortened .308Win.
.223Rem is out.
6.5grendel and 6ARC are based on a 6ppc which is based on a Russian military cartridge.
To the best of my knowledge that leaves most magnums(300Win has been used by the military) the .284Win, the .222Rem and .222mag, 30-30, 25-20, 22lr and some much less used black powder cartridges than the one that I named.
I hate to say a 22lr because it really leaves out big game despite the fact that it’s been done.
Ask a poacher or an Eskimo, and the answer is definitely .222Rem. The .222mag would only be better with a tighter twist and it never got any traction.
30-30 seems like the obvious winner, BUT for western hunting, no matter how many people use it, I have a hard time labeling it “best”. It’s probably the “best” non-military cartridge for hunting in the east.
I can’t name any magnum the “best” if a non-magnum that is suitable for moose and bear exists because there’s just no need for a magnum for 90% of hunting.
30TC just didn’t get any traction, but being a civilian equivalent to a .308, it gets good consideration. Why they throated it so that a loaded cartridge would actually be longer than a 308Win is beyond me.
6.5CM is seriously an excellent cartridge. Again, why the long throat? You use a short enough case to get modern bullets in a magazine, but then throat it so long that they no longer fit? I lean toward recommending 156gr for a 6.5mm on elk, moose and bear, and a 6.5CM is a little small to win the “best” with bullets that heavy. With a 130-140 I can’t call it the best for elk, moose and bear.
It looks like the .284Win is the winner! What can you not kill with a 168-190gr 7mm? Good barrel life, technically usable in actions other than a long action, could be used in a lever action, can use bullets heavy enough for anything and light enough for deer, what else were you looking for?
Well, I’m looking for brass that doesn’t suck, and I don’t mind a military based cartridge, so .280AI for me. Thanks.
I think the 6.5CM (and 6.5-284 if you want to allow it as American) are VERY close to the .284Win if elk, moose and bear are off the table, or if you’re not going to go heavier than 168gr in a 7mm.