RugerHawg, you should buy a box of each and shoot them. Don't shoot the barrel hot. Your rifle will tell you what it likes.
Having killed a few cow and bulls, I can tell you that I like a bullet that puts a lot of shock on the animal, and I will do what ever it takes to not put a bullet though a shoulder.
I used 7Mags with 140g Nosler partitions and 160g Speer Grand slams. For cow, I used a 243 with 100g partitions at 3000. I never had any problems but we rode mules and shots were not long.
Always, choose your shot or don't pull the trigger. I even killed two big bulls with a 140g nosler ballistic tips in the 7 Mag, and they flopped on the spot. Shots on these two big bulls were dead center of the body from length and thickness of the brisket. One bull kicked once, the other never kicked, about 150 yard shots.
We killed a number of bulls and cows in the late 70's and early 80's when we were young and dumb with a 7x57 shooting 140g Sierra's...never any problems but we were very experienced shooters killing thousands of jack rabbits per year at all distances.
I always sighted my rifle in at 200, knew the drop to 500 yards with an index card that I had taped to the stock.
I hunted with one guy in Az that shot a 7 Mag with 175g Sierra btsp @2900 fps, and that bullet really impressed me with how it penetrated. We butchered all our animals.
Elk never impressed me at being hard to kill at the short range distances we took our shots at. However, you are in for the worst possible tracking job you could imagine on a gut shot animal or one shot in the hind leg.
Do some serious planning on what you are going to do and how you are going to handle an elk once you get it on the ground. It is best to butcher them on the spot, bone the meat off the neck. Plenty of ice chests, large plastic bags, and a good knife or two, or the ability to touch up a knife with a steel. We never used a saw, ever.
Late afternoon kills are a real pain in the butt for many, many reasons. Plan on having lots of light for this occasion.