Don't forget the .340 Weatherby, .338-.378 Weatherby, 8.59 Galaxy, 330 Dakota, .338 Canadian Magnum, .338 A-Square, .338 Excaliber and finally the 8.59 Titan. These are all powerful .338s and they ALL suffer the same thing, brass availabilty. The 338 Lapua wins due to ease of acquiring brass. THAT is it. All the others are in the same ballpark. Even the lowly .338 Winchester Magnum can compete. These days, I'd stick to a 300 Win Mag and magic bullets for long range. Were I capable of accuracy at 1200 yards it's unlikely I'd shoot due to the lack of positively identifying the target. And much more significantly, there are very few instances I can contrive in my mind for the need to shoot that far.
OP, there isn't a nickle's worth of difference. Brass is where it's at.