Here is a pretty good write-up on the subject:
If I recall, Bias-Ply tend to bounce more, by wag/wander less and can handle heavier loads. Radial have a smoother but tend to wander/wag more. Radial also have weaker sidewalls which handle less load, but also have better tread wear and lifespan. I think I recall hearing that the sidewall strength on the biasply also make them less apt to roll on corners, but I couldn't find anything documented to prove that, so i'll treat it as anecdotal.