In answer to the original question, yes a 30-30 will kill an elk, within the limits of the caliber. I shot a bull at 65 yards with one and he ran maybe 30 yards and piled up. My grandad killed several moose with one. As stated, the 06 is a better round for the job. Better doesn't mean the other is no good.

I would base it on how well the boy can shoot the gun. Most shots in the field are not like a bench shot and even shooting sticks and bipods are different. If he can shoot more accurately with versatility with the smaller gun, go with that one.

In the end, his confidence in the firearm will have probably more influence on the success of shots then the caliber.