I switched from 15" to 16" so I could get a larger diameter tire. Running 7.50R16's on the back, 8 ply Dayton mud & snow. Tire man told me not to go under 45 psi to improve stability, I air them up to 70 when I haul. They can squirrel around on the wrong pavement. Part of my problem is I'm still running bias ply tires on the front.
As far as handling, the main advantage with radials it that they allow you not to get stuck in ruts in blacktop. They do make steering harder, and they can make you squirrel around some. On a concrete surface, bias ply tires actually handle better, but the reverse is true on blacktop and gravel.