Byass ply actually tends to get the nod for off road ability. They flex better and gain a bigger footprint. I am sure the tire info I have is a bit dated. I bet radials do just as good now a days.
The down fall as mentioned before is road noise, handle like a water balloon. They also get flat spots over night if cold and take a few miles to get rid of the square tire thump.
I bet with radials matching the off-road capabilities I would stick with nothing else. Maybe if I needed a speciality tractor tire.