The additional training a Child and Adolescent Psychiatrist receives places their level of expertese in treating young persons far above that of a general psychiatrist.  This expertese goes beyond simply treating children, but allows the psychiatrist to evaluate the childhood of their adult patients as well.  Furthermore, paying particular attention to a family structure is the purview of the child psychiatrist, and can add depth to any diagnosis and treatment plan you may receive.  Dr. Kelly explains it further in his book:

"Part of the requirements for general psychiatry training is that, at some point, trainees must spend two months working with children and adolescents.  The form this work takes, however, can be highly variable.   At some programs, first-year trainees (called interns) may only have to observe a clinical session once a week, leading to a thin experience.  Alternatively, they may work in a College Counseling Center or somewhere similar, which certainly doesn’t help them when the patient is a 12 year old.  For psychiatrists interested in treating younger patients, there is a separate training that follows their general psychiatry residency. Called a fellowship, it entails two additional years of working exclusively with children and adolescents."

You know who makes the best adult psychiatrist? A child and adolescent psychiatrist.
— Chairman of Psychiatry at Harbor-UCLA Medical Center

"One thing that many people don’t know is that no authority requires psychiatrists to receive board certification for treating younger people (and there are psychiatrists who decide simply that they’d like to add younger people to their patient list, without having any sort of experience in the matter).  In fact, any licensed physician could in theory open a psychiatry practice with no experience at all.  Therefore, it is up to you as an educated consumer to ask any potential providers about their training and board certification.  You can also go on to the American Board of Psychiatry and Neurology website (abpn.org) and look up the current status of any physician you are considering seeing."

- Adolescent Depression: A Guide for Parents, pages 299-300