I’ve used 30-06 180gr partition, 7mm various 150-160 grain bullets, 300 Weatherby 180gr TTSX from 11 yards to 550 yards for 15 elk. Helped with several more do not inexperienced but not the variety of some here.
If you are comfortable limiting your shots to less than 300 yards with good angles not much difference between 308 & 300 Win Mag. If you want to extend the range or take a tougher angle through bone or more chest the 300 is your better choice. My elk hunts are expensive trips with limited shot opportunities so I use a magnum with a stout bullet.