OK, obviously the tire you are running is gonna make a big difference with what pressure you feel comfortable with.
The terrain and other variables should also enter into your decision.
With that in mind, the 35" Toyos on my truck have a thick sidewall and are just broken in, 10,000 miles.
I still believe that for the most part, the lower the pressure the better the traction. I have been looking for the balance of all around ability while remaining as safe as possible.
My conclusion only applies to my rig, the Toyo's, and in Moab. (frankly because I'm hooked, it seems to have it all, and as close as it is to me, why drive anywhere else?)
Now, I ran Poison Spider Mesa with 13 psi. Good traction, and some good flex in the sidewall. I ran Metal Masher with 12, about the same. Hell's Revenge and Seven Mile Rim with 11. I also drove highway and freeway with 11 psi. For me, 11 psi is safe and provides the level of flex in the sidewall without worrying about the bead. I had all the weight of the vehicle on two tires at severe angles, and I didn't worry about the beads at all. 11 psi provided great traction and conformed around the rocks well.
I personally wouldn't hesitate to run even a little lower in sand or for enhanced traction if required.
Sorry for the long post, maybe someone else can use the information in this thread someday.