Sure you'll get lots of feedback on this one. Here's my take for what it's worth.
Radial.... More flexible sidewall, larger footprint or contact patch ,usually a smoother ride, usually long wearing, sidewall more easily damaged in rough terrain, generally more expensive, sometimes benefit from larger diameter wheels because of the softer sidewall.
Bias Ply.... Stiffer sidewall, less roll in hard cornering, most consider the sidewall better protected because they don't bulge like a radial, cheaper than radials, generally considered more rugged for heavy abuse.
Radial.... More flexible sidewall, larger footprint or contact patch ,usually a smoother ride, usually long wearing, sidewall more easily damaged in rough terrain, generally more expensive, sometimes benefit from larger diameter wheels because of the softer sidewall.
Bias Ply.... Stiffer sidewall, less roll in hard cornering, most consider the sidewall better protected because they don't bulge like a radial, cheaper than radials, generally considered more rugged for heavy abuse.