I notice that there are two ways through passage 11, a western route that appears in the guide book and an eastern (newer?) route that appears on the ATA interactive map. What are the pros and cons of these two routes?
As I recall, the "official" route (the western route) as you call it, goes through the Wilderness of Rocks (WOR). Very challenging, if not impossible for horses. That's another reason for the re-route.
The last few miles of the Pusch Wilderness Bypass - the Crystal Springs section - is a challenge! I do not think a horse could make it through there. Bikes would have a time as well. The other trails of the Bypass are great although Butterfly has a big elevation change. As a hiker, stick to the Wilderness. It's beautiful!
My mule “Rosie” and I have ridden the Wilderness of Rocks trail looping around to the Lemmon trail many times. Yes there is some rock climbing with some slick spots, but mules are the four wheel drive version of the equine world. They are half donkey and from that they get their intelligence and are sure footed. They have small feet and they watch and place them very carefully.