Interesting. Depends!
If going on an elk hunt I would take one of three rifles I currently have, a 9.3x62, .375/06IMP or my M70 .30/06.
Likely would be my '06 loaded with 180gr. Hornady SST's @ 2,745fps.
I would not shoot an elk with a .357, whether in revolver or rifle.
A .44 rifle would be minimal imho - & that loaded with a 265gr. Hornady FN @ about 1,700fps as far as pistol ctg. go. I'd also go along with a .356 Winchester, 220gr. @ 2,350fps, or even a 250 RN at 2,150fps in a model 94, or same in a
.375 Winchester with 220gr. Hornady @ 1,900fps or higher.
Or - .45/70 M86/71 Pedersoli, .50/95 M1876 - either of those would work fine.
Hate to admit it, but a decent .270 with 130gr. TTSX or 150's would also work just fine.
Of course, so would a bunch of other rounds, if loaded with decent bullets.
7x57, .308, 8m Mauser, 6.5's. Even the 6mm's loaded with Barnes or other premium bullets have been used around here, VERY successfully on elk.
Anything that would work well on moose, will work well on Elk. Bullet placement is of paramount importance. Elk are tougher than moose. 1 lung on am moose and don't push him & he's yours inside 100yards from impact. An Elk can & will go a LONG way with 1 good lung left, pushed or not. More likely to run than a moose.
Just be good with the rifle, so accurate bullet placement is the automatic result.
I think buying a new rifle for a special hunt, is not a good idea. Use one you are familiar with.