It seems to me that the OP isn't that much interested in more balanced views if it comes down to choose an really appropriate caliber / round regarding his original question is he? Then, beyond any doubt the recommendations made by @Feenix and @Frank in the Laurels are right on!
There is nothing better to find as a superb 8mm Rem Mag looking to the USA IMHO. In Europe you'd have luckily some more decent 8mmS / .323 choices. The "Big 8" delivers as much energy at 500 yards as the .308W does at the muzzle ... Even with ordinary bullets like Nosler AB etc. it's no problem at all killing huge moose at 1k. 220gr bullets get easily accelerated to more than 3000 fps. CEB and others are already manufacturing LR - bullets for 8mmS / .323. Some guys who are "lifetime - hunters" as Gregg Boddington are swearing on the "Big 8", and those guys really know what they are talking about. I for example have been using various types of 8mmS throughout my whole life as hunter / shooter, and nothing really nothing comes close to them. You don't need any .30 or .338 cal, because the 8mmS is doing the same or better. If you won't give it a try you'll never experience something outstanding good.