The disadvantages of these tours are that you're not always at a location at the best time of day, and the stops are short, so you can't devote much time to photography. Several types of Indian-guided tours are offered. Half-day tours go through Monument Valley and Mysterious Valley. While Mysterious Valley contains more ancient Indian ruins and artifacts, the Monument Valley tour has more spectacular scenery and you still get to see some Indian ruins and petroglyphs. A special eight-hour tour takes you through both Monument Valley and Mysterious Valley.
Tours go out in the morning and in the afternoon.
Since midday is a pretty dull time to shoot, the stops during the last part of the morning tour and the first part of the afternoon tour will be pretty poor, photographically. If you must choose one tour, the afternoon one is best. If you have more time, consider taking both. The tours that leave from the Visitor Center take fewer people, possibly allowing you more photography time. You ride in a small bus that carries about 20 people.