I agree the initial cost of the brass should not be the deciding factor for this build. As far as brass quality, if you want your brass perfect you will do less prep to the Lapua brass. Neck thickness, primer cockets , flash holes all will be more consistant on Lapua brass. I have had new 30-378 and 338-378 brass that needed primer pockets reamed before a primer would go in consistantly. Not all, but some, but don't worry, after the first firing it will be looser and this is the area WBY brass will fail first. My 338 Lapua brass with 15 loadings on all the primers come out wih a "POP" and I seat with a hand primer tool and they all go back in with the same pressure. That impresses me.
But still,,, this should not be the deciding factor either. It
IS about velocity! Do you want the exta 200 FPS with a 300 gr bullet? Velocity is great, but probably not necessary to fill your needs with a .338. Are you going to take game past 1500 yards? I still have 1427 lbs of energy at 1500 with my 338 LM. Are you going to target shoot past 1900 yards? I am still super-sonic at 1900 with my 338 LM.
Here is a neat calculator to figure the cost per round for each very easily.
Handloading Cost Calculator
Know that the velocity comes at a higher price than the brass. Barrel life will be shorter with the 338-378. You will be using 10 to 15 gr more powder with each firing.
The velocity is nice, you will have less drop and you will have less drift. The drift is the most important to me. But understand they both can be dialed for and when they both connect, that animal will not know the difference in 200 FPS. And I doubt any target will either.
Figure your total cost including barrels, gun smith fees, powder and brass over the life of a barrel and look at cost per shot. Then decide which you can afford to shoot the most. The amount of time spent behind the rifle will will pay off more than the gained velocity.
For all of the above I am happy with my 338 Lapua.
Jeff