Either would be suitable for youngsters. The 7mm-08 would be the better choice, if game larger than white-tail is anticipated in the future. The 7mm-08 is the ballistic equal of the famous 7mm mauser in terms of potential lethality, so long as the bullet is placed in the vitals.
In other words, the 7mm-08 kills much better than it's printed paper ballistics would lead you to believe. The cartridge is very accurate, as it was originally developed for metallic sil. Shooting from ranges of 100 to 500 meters and still have the energy remaining to topple over those heavy steel targets @ 500 meters.
The recoil is mild, cases are easy to load, case life is excellent, wide variety of 7mm bullet weights & propellants are available.
However, for varmint elimination & small deer, the .243 winchester is "da-bomb"
guru1911