I would say both cartridges are a wash as far as intrinsic accuracy.
The 243 will have a stiffer barrel than the 7mm-08 due to the smaller diameter bore, which certainly lends itself to better accuracy.
An oft overlooked part of shooting for accuracy is recoil. With a light recoiling rifle, one can concentrate on firing more easily without worry. Light recoil also means being able to hold the rifle without a death grip, which generally helps usable accuracy.
With the 243, it wouldn't be tough to start the kids on 55s loaded to 223 velocities, then work the loads up as they see fit, transitioning to a deer bullet when the time comes.
