Elmer Keith professed that the .270 rifle was all you needed to hunt any game in North America. Factually he is correct however it depends on the kill zone and bullet placement. I always tended to disagree with his thinking because when hunting elk and bear, I always wanted a humane kill. I did not want the animal to suffer. Granted you will not always get that kind of shot, but you try to work yourself around to get a good "kill zone" shot. A .270 is a great rifle for mule deer and animals that size. However for elk, and for long distance shooting I always preferred my 7 Mag and 175grn. Nosler partition bullets that I hand loaded. A .300 is a good elk round also but I also know of an instance where the .338 proved to be too much for an elk. We were in New Mexico and a friend of mine borrowed a .338 and shot a bull elk, bullet passed through the heart/lung area and hit another elk. We were on tribal land and had to get a tribal game warden to come down and verify that he did not poach the elk (the 2nd one down). I believe he was shooting a 220 grn bullet if my recollection is right. For big horn sheep and elk the 7 mag will do a fine job as will the .300 mag. However most hunters will want to preserve as much meat and antlers/horns if possible and should a head shot occur both calibers will have a devastating effect. If you are meat hunting only, then a head shot is the best way to go and you haven't lost much meat. Sometimes a larger caliber is not always the most effective way of taking an animal. A 7mag or .300 will reach out to 400 yrds. and still give you a good kill although that is a long shot. It can be done! Big horn sheep have a smaller kill zone so my intention would be to move in as close as possible but bighorns like their space and they will go high to get away from a hunter if you are spotted. Just MHO only!
Tommy