the "modern refinements" are really focused almost 100% on long range performance. If you are shooting under 400 yards with anything short of souped-up benchrest equipment, you wont really see the improvements nearly as much with lead bullets, and you will think its all bun and no burger. However, 400 yards IS long range for a copper mono, so since it sounds like you are shooting monos you might benefit from a bit of the new school. The old-school flat-shooting cartridges such as .270win designed for maximizing point-blank range (ie before dialing scopes were really a thing) may actually perform better for you with copper monos, ie a 270 shooting a 130 mono has a higher BC than a .308 shooting "the same" 130 mono, so even if they have the same muzzle velocity (?? I'd be surprised if they did given the difference in powder capacity) your maximum terminal range is going to be longer with the 270, and may even be longer with the 6.5cm even if its starting slower, simply due to the higher BC of the same weight bullet. Even within the same cartridge there's a difference, ie in my 270 a 129 lrx retains velocity farther than a 130 TTSX. I would be extremely surprised if you can get a factory-loaded 130gr copper mono fired from a .308win to retain sufficient velocity at 400 yards to be truly reliable, but that's easy with a 270, just for instance. Personally I woundnt worry about it being "larger", in my limited experience that's not noticeable in how effectively they kill; it's the impact velocity that warrants worrying about.
How much are you shooting that you are worried about barrel life? If you shoot that much, is getting a new barrel every so often that much of a additional burden?