I'm in the same camp as Ronster and Yellowknife. I've been in on probably 25-30ish moose kills over the last 22 years here in Alaska. Moose aren't that hard to kill. Poke a hole in the lungs, they'll act like nothing hit em. Takes about a minute for lungs to bleed, BP to drop and for the big guy to topple over. Like any other critter the only "bang flop" is a CNS hit. A 243 with a 100gr Nosler will do that. Heart shoot one and they tip over pretty quick, usually they do a back flip. I've seen it a few times. My bull last year was the most recent. A poor shot with any caliber will give the same results.
Lots of Moose killed with 270's up here. 30-30's in the bush communities. I'll be chasing them around with my 45 Colt wheel gun this year with 355ers at 1200fps.
No need for an "uber-magnum" to kill a moose. If you are confident in you trusty ol' 308 go kill a moose! Poke a 30 cal hole through the lungs and let the work begin!
The only exception I can see is hunting moose in the hills or flats where a guy could potentially have a 3-500yd shot and the ability/scenario to take it. A heavier bullet will carry more energy for better penetration and not be as effected by wind as much as a lighter bullet. My longest shot was last year, 365yds. 200gr Accubond from my 325wsm. Heart shot, back flip. I shot one at 315yds once with the same load and broke the spine.
But... "the big moose hunt" could be a good excuse to buy a new gun

Like say a big bore levergun like a 45 Colt, 454 or a 45-70.