The shake and bake tour is an open truck with seats for 20 or so on the back. It went from Thunderbird lodge, near the entrance to the park and bounced quickly through the park often in the blazing sun. The private tours are in a 4wd vehicle with a guide driving who will tailor the trip to your interests and will talk to you about the canyon, history, life now etc. When we went our guide knew that DH was interested in seeing petroglyphs and pictographs and she had a small mirror that she used to catch the sun and point out the ones that were in less obvious places. Get a guide, either in your hotel or at the NP visitor's center.

I'm printing and saving this whole thread to refer back to as we make our plans. Immensely helpful. Thanks to all who have responded.

You can't go wrong with either destination. I love them both so it would be a hard decision. I see you have decided on Canyon de Chelly.

We did the "shake and bake" tour. We did it in late May so it wasn't very hot so we didn't bake. All we had when we visited that year was a motorhome so we didn't have the option of doing a private tour in our vehicle. The roads in the Canyon are not paved so I don't think I'd want to take a rental car into the canyon.

Utahtea