we are talkin about all these nice cannons here, but we are forgetting the cost of recoil. I have only been shooting for about 3 years now and Im still not used to the heavy recoiling magnums (my largest is 375 h&h). I once shot the 30-378 and..... hated it, that was, too much.
338 Lapua is pretty expensive, both the rifle and the ammo. And Im pretty sure your gonna end up getting one with a muzzle break and that means, your probebly going to need hearing protection even when your hunting lol. On the other side of this, you got the 375 H&h, recoils about 2x a 30-06 (almost), cheap ammo, and decently priced guns (about 800-900).
both rounds hit hard, esspecially for the type of hunting your going to be doing (shots will be less than 200 yards), a 375 h&h is the prefect match. But if you don't like its "rainbow" trajectory, get a 375 RUM or 378 wby. that way you can have that 375 bullet with very good trajectory, however your shoulder will hate you for it.