Read through comments quickly and will add my opinion on something I didn't see mentioned. Since the edge first became popular, a few slow burning powders have been added by manufacturers and this closed the gap the 338 edge had over the 338 RUM. When the edge first became popular, the standard load was H1000 to get the 300SMKs to 2800+. With other slow powders out there and properly throated 338RUMs, these custom 338 RUMS can now get 2900FPS. And with that said, with the edge being throated further out and custom mag boxes, it is doing over 2900FPS as well. in my opinion, whether you go edge or RUM, I don't think the difference is what it use to be, and you cannot go wrong either way, so long as it's being throated appropriately. And while I think a 338 lapua is very cool, not sure the added cost of components and larger action is worth it, but again, obviously a very awesome round and if I had one I'd dig it.
Put a 28+ inch fluted sendero contour on any of them with a good break and it will be an easy, shooter friendly rifle. The one I use is an edge. Currently loading with imr8133 and getting 2900 FPS with 300 grain Berger elite hunter. It drops bulls in their tracks.