Of the cartridges listed, the 338 Win Mag would be my recommendation based on first hand experience with the targeted species.
I have taken moose, elk, grizzly and bison over the years, from 20 yards out to 370 yards with 300's (Win and WSM), 338 Win Mag, 35 Whelen, 9.3x62, and 376 Steyr (ballistic twin to milder 375 H&H and Ruger loads with 260/270 gr bullets).
I can tell you that while bullet placement is everything, that there is a significant difference in the on-game performance on bison between the 300 with 180 gr bullets (2) and the 338 Win Mag with 210+ gr bullets (3). The 338 has the next level of impression that a big bull bison just doesn't shrug off as easily. The 376 Steyr (2) also smacked a large bull bison at 200 yards (longest shot on bison w/ this rifle) with good authority. The extra frontal area and weight gave great performance, with each jump up in caliber. Quicker, cleaner kills.
While I like the 35 Whelen, and really like my 9.3x62 and 376, if I am facing longer shots, the 338 gets the vote.
Having shot a number of elk with the 300 and 338, I also find that the 338 also provides quicker, cleaner kills compared to the 300. (have taken 2 dozen elk with cartridges ranging from 6.5x55 to 376 from 70 to 475 yards).