They are fine on or off road. The sidewalls stand up a little better (or less dependant upon your out look).
There is a reason they are making a comeback in the market and you will notice it is all in radical offroad tires.
I do not like radials in the taller sizes. But thats just me. When I was first driving radials were an expensive family car tire.
You will probably not notice the difference between the two on the road, unless you have driven the exact same size tire with radial construction. Some people make the mistake of going from a 10.50X31 non agressive trend all terrain radial to say a 12.50X36 heavy lugged bias, and blame the entire difference in ride on the bias tire. The only real difference in ride will be a slightly rougher ride in the bias. Road manners for and identical size and tred pattern radial are almost the same. In fact on the taller tires the side wall flex of the radial can be a little anoying on taller tires.
Offroad in mud an equally aired up radial will float better than a bias.