Both are inherently accurate cartridges, but when you say "elk" I believe that you should go with the .300 WSM
. Lots of really good, accurate, reliable game killing bullets in .30 caliber. Factory 180 Failsafes for instance.
I did a test of the .300 WSM a while back and found the factory ammo to be extremely accurate out to 1000 yards. Shot a GA Precision rifle with a Nightforce NXS on it and got some three shot groups out at 800 yds that were at or very close to 4" with 180 Failsafe ammo. Have never seen Failsafes shoot that well. I was impressed with how well all of the factory loads shot.
A M-70 COYOTE in either caliber will be an excellent hunting rig, but I believe that elk are best hunted with heavier bullets that penetrate.