Have to agree with eroyd, at least in part - - -
I think that, shooting such a "tradional" old west style animal, I'd like to use an appropriate older-style rifle. Or, at least, an old model cartridge, such as .45-70.
As far as just taking the animal in aproper fashion, though, I wouldn't be at all shy about using my .338 WinMag or, even, a .30'06 with proper choice of bullets.
One old friend, now departed, did it both ways--Rem Rolling Block .45-70 with a long brass scope sight, shooting 500 gr handloads. Then with a Model 70 Win lightweight '06, with factory 180 loads. Both one shot kills.
Best,
Johnny