I have found from experience that there is a huge difference between the .300 RUM and the .338 win mag. A huge huge difference.
The .300 RUM and the .338 win mag both are capable of taking any brown bears from a long distance. These two calibres are high ballistic coefficient bullets which maintain their energy for a long time downrange. And brown bears take a long long time to die, so from a long distance is where you would only want to engage them.
But the difference between the .300 and the .338 is very painfully obvious every time you shoot it.
And there are smaller variations of cartridges than the .300 which work well on elk or moose or mule deer or caribou.
So unless you are hunting brown bears you really do not *need* a .338 whereas if you are hunting brown bears the .338 is probably the best of the *lite* calibres for this animal worth considering due to its flat trajectory and power retention downrange, compared with the bigger fatter bullets commonly used on brown bears.
Hopefully that clears up some confusion that some others might have had.