I agree with both of you especially since I volunteered at a day camp before I worked at an overnight camp.
And I felt like I was basically babysitting, but maybe I was wrong.
With overnight camps, you get to know each and everyone of your campers and how they are when they came and how they have grown through a week or so of camp. I would never go back to my daycamp after my experiences at overnight camps. I learned a lot of leadership through my overnight camp as well as many more skills that will be very useful throughout the years.
And day campers dont get to experience a real campfire, unless they have a sleepover for a night or something. At camp you get to experience so much more - camp songs, camp food, camp life, etc.
Correct me if I am wrong about some of this, but this is my opinion.