personally (for me) one of the bigger factors with young children is that the practice is without a doubt set up for pedatric patients While I am SURE without a doubt that many professionals who see a complete family just fine, first time out especially if you doing it because you have a concern compared to just a routine visit to start your child out, someone who works almost exclusively with children would be my choice).
I guess that's the other thing if you have a concern that isn't just hey my child might be near sighted or far sighted, I would probably go with the opthomalogist but again I would pick a pedatric optometrist over a family opthomalogist
http://www.eyecaresource.com/professions/ gives a nice little description of the differences in training without putting one or the other group down (which a lot of sources do

)
In the end I don't think you really can go wrong, if you have a good doctor
Learn from the mistakes of others. You can’t live long enough to make them all yourself.
Eleanor Roosevelt