The inception of the .308 Baer came from the 8 mag case. It is now based off the .300 or .340 Wby case. the .340 is the preferred case as it gives a longer neck over the .300 Wby. The STW case can also be used in a pinch if need be.
Aside from the fact that the .308 Baer cartridge has held the world record group size at 1K, it is significantly
more efficient than the .300 RUM. I have many custom rifles
chambered in both .300 RUM, and .308 Baer, so my experience is hands on.
The .308 Baer gives up nothing to the .300 RUM. It will propell the same weight bullet, at the same velocity, and do so with roughly 8 grains less powder. That's a testament to the efficiency of the case. ES will be on your side every time with the more efficient case.
The brass offerings for the .308 Baer, Norma and Wby, was better than the RUM until the advent of some of the custom RUM brass. So I would call that a wash between the two. If this is a hunting rifle, then I would suggest a standard no turn neck, as you can find the .300 Wby cartridges worldwide, should your friendly airlines be kind enough to lose your hand rolled cigars...
Forget the argument about the belt....they both headspace off the shoulder.
So in summary, if you want a off the shelf cartridge that has proven itself in the field, then stick with the RUM.
If you want the more efficient case design that has proven itself in both the field and in the competitive shooting world, then go with the .308 Baer.