My parents started going on some Duke sponsored trips in the late 80s and did a few different ones over the years. They enjoyed them.
My take on what they told me about them was that the people on the trips tended to be better educated and well off than you might find on an average trip. The trips usually included a professor or some sort of other topical expert that they felt brought added value to the trip. They also liked trips put on by the Smithsonian for the same reason.
The people on the trips do not necessarily all have a Duke connection though. Sometimes the amount of Duke affiliated people is not enough and it will get merged with other people, possibly from another college travel program.
The one I remember the most was when they went on one that was a raft trip down the grand canyon. The week of the Duke group got filled up, so they ended up going the week before or after with the same operator. Part of the group they went with was an advance team from the CBS show 48 hours for a show they did in 1990.
You do pay a premium for these trips vs. what you could find on your own.