My opinion is pretty strong in favor of the pediatrician.
I spent 9 years in doctor's offices, mostly family practice, as a pharmaceutical sales representative. The majority of a FP's practice is adults, and the volume of information they need to know for things like Diabetes, Cardiovascular disease, etc. is overwhelming just for adults.
It's almost impossible for them to be well-versed on pediatric medicine as well as a pediatrician. While there are a ton of great Family Practitioners out there, we believe strongly in taking our children to a Pediatrician because that's they're specialty.
I'll be travelling to the American Academy of Pediatrics national meeting next weekend in San Francisco. There are so many new guidelines, knowing which medications can be used in adults (usually anyone over 16) vs. children. I would just personally feel more comfortable with someone whose entire practice was dedicated to that.
I also selected to go to a lymphoma expert when diagnosed with cancer a few years ago instead of a general Oncologist - it just made me feel more comforted that he was more in the "know" with how to treat my cancer which is still relatively rare compared to others.