AP rifle
Thinking you need to pick caliber first, then a launcher.
Since you list moose, that is a pretty big critter, and I read they can soak up a bullet surprisingly well sometimes. And an elk is a pretty big critter too, not that I've ever shot either, or otherwise get the chance.
But for big critters like that (heck a big bull might go what...1200 lbs plus, Wiki says 1500!!!) I'd want .30 cal, and that means '06 or .308. In the field, the two are almost indistinguishable and performance one v. the other can come down to individual rifles. If I were to assail a moose I'd shoot some type of space bullet at it, one of the mono alloys, or minimally bonded or partitoned Nosler/Swift. If I had to go traditional cup/core, I'd shoot a 180 gr +.
Its all words though, 'cause I sure don't see a moose or elk hunt in my future.
I sure plan to shoot a bunch more whitetails, some hogs (maybe lots, that seems like it could be arranged) . For that a .30 is a bit much but has been getting the job done for years. I like the .308, and I like the scout rifle concept as a GP tool. Ammo is plentiful, the .308 is efficient from shorter tubes, and the short action family might tote a bit easier afoot. I might set one up with the option of scoutscope/dot and a more conventional higher X count scope if I were to wander onto more open country for a hunt, and heaven forbid were limited to one rifle.