I would agree with heather on this one.
if you are with children, you will need to bend down, or reach down with one hand frequently.
while around your neck might seem good, when you bend down, you will hit the child on the head with the camera. OOPS
shoulder bags sound good, but they put the load off center on your body, and after a while you get very sore. Additionally they will slip off if you drop one shoulder (holding a child's hand for example)
Backpacks spread the load over your body, usually put the load where it belongs, your hips (if they are good bags) and stay relitively in place. While perhaps inconvenient for access, they are probably the best for comfort. Also, you can use the back pack for carrying otherthings too. Drinks can be as heavy as lenses, and don't forget a small first aid kit. Kids do get scratched and scraped due to falls when hiking.
While I don't have much experience with them, Sling bags also could work, because by nature they do distribute the load over a broad area, and may be better for access than a back pack