As a day camp counselor I think day camps are great. You spend your entire day with your own group, you eat lunch in your own group, sit in the bus together with your own group when going on a field trip, you do all activities together, and believe me, you get to know your kids very well.
The days are absolutely packed at the day camp I work at...you don't have the afternoon nap...you go from activity to activity and do a maximum of activities during the day.
I think it's better for the younger kids to go to a day camp. In my personal view a 1st grader, and even some 2nd graders are not ready for overnight camp at all. Why would you want to force a 6-year-old to overcome homesickness...that's a battle you can start to fight later, just let the kids do all the fun activities a camp can offer and sleep safely in their own bed.
I think that from an older age on it depends on the child which kind of camp he or she'd enjoy the best and would get the most out of. You can't say only an overnight camp gives the ultimate camp experience. What if you hate overnight camps?
I remember that as a girl I hated overnight camps from the pits of my soul...I wasn't the brave kind of person. But in the country I'm from we don't have day-camps, but I think I would have loved it.....
