ORIGINAL: Rammer
I don't have either one, but if it was me I'd go with the 300 Win Mag. I am not sure how that short, fat lil case would feed in an auto rifle.
That would be my concern as well. The BAR has been made in .300 Win. Mag.long enough that the bugs should all be out of it by now.
As for accuracy, short, fat powder columns lend themselves to more uniform ignition, as there are more powder grains closer to the flash. In addition, short actions are stiffer, again improving accuracy. I have no idea how the WSM's compare to the "standard" .300's, but I do know that the cartridges based on the .284 Win. case do tend to be easier to develop really accurate loads for than those of the same caliber that are based on the .30/'06 case.