Going on 15. Fair height. Slim build. He has shot my .30/06 and I think he is comfortable with either caliber.
Sounds a lot like what I was at that age. If he can handle either, then I guess there are only a couple of things to think about; is one cheaper than the other (gun/ammo), will it be used for other animals (start considering bullet weight ranges).
If you still have your .30/06, you may want to consider getting him one, you could get into reloading, save some money there, and have one set of dies for both rifles.
I am not trying to steer you towards the .30/06, just pointing out some things to think about as both are great rounds.