As others have said, they are really two very different kinds of experiences. Only you can decide which one you'll enjoy more, but do consider hot weather and crowds.
To visit all six of the chateaux you've listed within 3 days, you'll be pretty rushed. For me, paring it down to four (or five max) would be more doable. You will have a rental car, yes? Because public transportation doesn't cut it for visiting the chateaux. If you don't want to drive, then sign up for day tours that include the chateaux you like best. Using Tours as your base means you'll be centrally located, which is a plus for taking day tours, but be aware that driving in Tours can be stressful with a maze of highways and heavy traffic.
We stayed in Azay-le-Rideau at the Hotel Biencourt and absolutely loved it. On one day we drove to the Fortress of Chinon, which was a wonderful contrast from the more luxurious chateaux that the Loire is famous for. It has lots of informative signboards (ties to the Knights Templar, Joan of Arc, and Eleanor of Aquitaine), indoor exhibits, and motion-activated sound effects. We didn't have time to do the walking tour of the old town (described in the RS guidebook at that time; not sure if RS still has this), but it looked lovely from the heights of the fortress.