Personally I think the .338 Lapua kicks more than .375 Ruger, .375 H&H and .375 Weatherby, but not as much as the .378 Weatherby(only fired one rifle in this cartridge, so hard to compare).
The downrange ballistics of the .338 Lapua is clearly better than all above because it shoots bullets with much higher BC.
225 grain .338 barnes ttsx has 0.514 bc, 265 grain .338 barnes ttsx has 0.575 bc and a 250 grain .375 barnes ttsx has 0.424 bc.
I really don't think the .338 Lapua is the ultimate plains game caliber at all unless you plan to shoot most of your animals at 400 yards and longer.
And to shoot a .338 Lapua at 400 yards and longer demands very much practice with it at long range.
And you will wear out your barrel rather fast when using max loads(as you should when shooting a .338 Lapua).
I promise you that it will be expensive unless you are sponsored
Inside 400 yards most people will be much better off with a less recoiling cartridge.
And if I wanted to use a hard hitter on plains game inside 300 yards, I would rather use my .375 Ruger that is legal for anything