Should I use screws or nails to hang 19/32" thick t1-11 panels indoors?
I would use neither. Since the panels are not used for a structural purpose and only need to be held in place, finish nails would be my choice. For a finish product, the screw heads or even the nail heads would be noticeable in the surface. Filler on this type of textured surface is not a good option.

But if those are the only choices you have, screws are the best choice, you can control the screw better than the nail for depth. Nail guns will overdrive the nail and create a deeper recess than needed.