I know I’m a late comer to this topic but it is very interesting to me as I shoot both rounds and have done so for over 30 years.
I’ll save space and not repeat what has already been said but just to provide an understanding of why actual recoil is more substantial in a 300 Weatherby than a 300 Win. Mag. Here are the four factors that affect recoil. (without getting into stock fit and any additions to mitigate recoil such as muzzle brakes and different recoil pads, stock fit, shape of cartridges, i.e; “efficient” VS “high intensity” etc…)
Raw recoil is calculated by having the following elements:
1) weight of powder charge, (not its burning rate)
2) weight of bullet.
3) speed of bullet.
4) weight of firearm.

The more powder, the faster the bullet the heavier the recoil. The lighter the rifle, the heavier the recoil.

As for the German hunter who had an ornate high end Weatherby in Alaska, in Germany, hunting is generally not a sport accessible to all. Firearms used are more often than not expensive. (Upwards of 20k and more). A great piece of wood is considered part of the firearm and regardless of weather conditions, it is used and isn’t a safe queen even with the most expensive rifles in the 100K range, ornate to the gills. It’s a different mindset. Although synthetic stocks are getting more popular in Europe, good wood is still prized and shown and utilized in the field.
In the U.S we tend to view a firearm as a tool, which it is, but not as a fine piece of jewelry capable of taking a brown bear. For us, generally that is…The uglier the bear, the uglier the rifle, because we like it that way. Differing viewpoints, no one is right or wrong.