First of all, I'm a hunter not a sniper, so to me, big bears are an under 200 yard shot and really, I much prefer under 100 yards, so I just don't need the velocity a cartridge bigger than the 06 case has for .338 bore. With the 06 case, the rifle holds one more round, and performs well with a 22" bbl., instead of 24".
I did try the .338win mag., and even a .340 Wby. before building my .338-06.
As for the Whelen, the 350 Rem. mag. pushes bullets at the same velocity as a Whelen and I owned/shot game with two different rifles chambered for that cartridge. A Rem. 600 and a Ruger 77, I wasn't happy with bullet performance in 35 cal., and went to the .338 for the MUCH better game bullets available at that time. I did shoot some big game with the 35 to find that out.
Keep in mind, I was putting a rifle together for bigger, big game, not deer and blk. bear...
SR