In my opinion, the 6.5 Creedmoor is miles ahead of the .243 as a big game cartridge, especially for larger species or longer range.
With that said, short .243 barrel life is usually only an issue in long range match guns that see a LOT of shooting. That's one of the reasons why the 6/6.5x47 Lapua has garnered it's devotees among the 1000 yard set. For a hunting rifle with occasional target use, barrel life shouldn't be much of an issue.
Unless you're completely set on a short action, the 6.5x55 Swede might well be a better choice than either the .243 or Creedmoor rounds. For a handloader with a strong modern rifle and quality cases, it has a power advantage over the Creedmoor, particularly with heavy bullets. The biggest advantage over the Creedmoor might not show up for 15 or 20 years when your son is looking for cases.
The Swede has been around for over a century and will probably be around for at least a couple more.
I'm not so sure about the market supporting the .260 Remington, 6.5x47 Lapua, 6.5-284 AND the 6.5 Creedmoor over the long haul. It seems like cartridges that are primarily promoted for target use have a fairly short "mainstream" life.
Target cartridges like the 6mm PPC and 7mm BR don't really die, but they're kept alive mainly by true believers that don't mind the hassle of forming their cases from other rounds.
Even if the thought of that doesn't bother you, who knows how your son will feel about it in 20 years?
Just about any reasonable .264" bore will be a far better "all around" big game rifle than a .243 Winchester.
The .257 Roberts or the Ackley improved version would be another viable choice.
My youngest son has been able to competently handle and shoot my 7.5 pound Sako .257 Bob Improved since he was 7 years old. The first couple of shots he took with it were with my 75 grain case forming loads, but at his insistence, he moved up to full bore 100 grain loads at almost 3300 fps the same day with no trouble.
I had planned to work up some lighter deer hunting loads for him, but it proved to be unnecessary.
He has since used the same 100 grain Nosler Partition load to kill a nice 11 point buck at 437 laser measured yards.
If larger species like elk are possible quarry, the 6.5's would probably be better choices, but the .257 Roberts Improved is an excellent, flat shooting choice for game up to mule deer size.
