Here's an interesting article and video comparing the use of natural light against off-camera flash. Quite different results between the two.
My thoughts? Neither is right or wrong, but they give a different look and it depends on what you are after from the session. I think the off camera flash gives an additional pop to the images that when done carefully can really enhance the shot. But also factor in that with family photography you sometimes need to be moving quickly and reacting to events, and off camera flash techniques require you to slow down, position equipment, and get the settings right - and that takes time, meaning it's not always possible. In my shoots, whenever it's possible, I like to use some additional lighting, but sometimes the situation doesn't allow you to that and you have to know how to use natural light as well. It's all interesting stuff and adds some complexity to a session!