You must use a magnum now to kill a moose. The rifles that were used a hundred years ago are longer capable of taking down a moose. The reason is over the years the moose hide has become tougher and standard calibers will not penetrate the now much thicker hide
While hunting moose in Quebec a few years ago the guide said most guys there use a .270. Of the two you listed would go with the WSM and probably 180 gr Barnes. I carried my .300 Win but got no shots. I had it loaded with 180 Hornady spire points.