the 7 rum will be better for elk past 800 yds. More case capacity means higher velocity, more energy on target and less wind drift.
However the 7 rum will have less barrel life and the long throating may make it difficult to get the vld type bullets to group well (large jump to rifling) although i have heard good reports with the 175 sierra matchking. The 200 gr wildcat bullet would be pretty good though.
The 7 stw will have less recoil and slightly more barrel life.
With your requirement of elk past 800 yds i would go with the 7 rum. The remington sendero ii would be a good place to start.