All three of those imaging methods are equally accurate for measuring limb length. X-rays do expose the person to some radiation. For a single X-ray that isn't much but if he will need repeated X-rays over time then an MRI might be better (no radiation).

MRIs also give detailed information about the bones and soft tissues. That might be helpful in your son's case. MRIs are more expensive than X-rays. You might want to check your insurance coverage as part of your decision-making process.

CT scans have decreased radiation exposure compared to X-rays. Their only other real advantage is in assessing leg length difference when the knee can't straighten out all the way. If that's not a problem, then X-ray or MRI may be your best bet.