In my opinion, anyone who asks on the internet which of two, what I consider minimum elk cartridges, would be better to shoot an elk at 600 yards, doesn't have any business shooting an elk at 600 yards. So my answer to the OP would be neither, cut that distance at least in half, and with proper bullet placement, either of those cartridges could quickly and humanely kill an elk.
I've killed a pile of elk, and I've killed elk with sub-.30 caliber cartridges, but I've never killed an elk at 600 yards, and I can't remember killing an elk at even 300 yards. My favorite elk rifle now is chambered in .300 Weatherby, and the last two elk that I killed with that rifle, I spotted at about 300 yards, and I then stalked to within half that distance and dropped both bulls in their tracks with a single shot each. I'm proud that my closest shot on an elk was 10 yards.
I go to our range at least once a week, all year. Part of every trip, I shoot one or two rifles from field positions at the steel gongs at 200, 300, and 430 yards. The Weatherby Vanguard chambered in .308 Win that I have now, I specifically bought for inexpensive, light recoil range shooting at these gongs. I enjoy laying down prone and shooting a string of 10 shots at the gongs at those 3 distances and ringing them with each shot. Every week for a month or so before I go on any hunt I'll also bring the rifle that I'll be using on that hunt to the range and also shoot 10 shots at those 2, 3, and 430 yard gongs with that rifle.
Elk are not bullet proof, but they are big animals that can absorb a lot of lead from poorly placed shots, or shots that did not penetrate into the vitals. A poorly hit elk can run for miles and be lost to another hunter or just lost and become coyote and magpie food. I believe that a mature bull elk is one of the most magnificent animals in the woods, and I believe that we, as hunters when we hunt, should strive to kill that animal as quickly and humanely as we can instead of trying to kill it as far away as we can or with as small a cartridge or bullet that we can.