Having loaded both - the 300 Win Mag gets the nod......300 WSM doesnt do well with the 180-200 grain bullets as far as load density / compressed loads go. This is cause the action is short and the bullets are long.....no where to seat the bullet 'cept in the powder room! The 300 Win Mag has more than enough energy at 500-600 yards to do the job.......provided you are using proper bullets....Barnes LRX / TTSX are my go to bullets! I'm Not an accubond fan but others like them. Another great choice is the Swift Scirrocco II.
If your serious about the weatherbys definaltley look at the 30-378, 300 weatherby, and the 300 RUM. and of course any of the big 338's. I use a 338 RUM (hunting) and 338Lapua (long range) and they will be a better long range round for your intended purposes. Bigger heavier bullets, better SD, roughly the same B.C. but carry a lot more energy at those longer ranges. Dont pass up on the 225 TTSX in the 338 as this is my go to bullet in the RUM and this year hammered a Spike elk at 475 yards and got just over 48" of penetration.
Going forward.......whatever you pick - .300 win mag on up....use the heaviest, best B.C controlled expansion bullets you can find and shoot accuratley. Also remember the worst possible shot could come in any hunting situation............ yup thats the one rioght up close and personal (<50 yards) you will need a bullet that can and will stand up to that kind of abuse!!! and also perform way out yonder whent that shot presents itself!!
Good luck in your decision!! (nice problem to have)