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Here is a quick wikipedia find about the two different types. Its seems like radials are stronger and offer a smoother ride and thus better fuel milage. But if you are going for traction i would say the studs should be fine
In the past, the fabric was built up on a flat steel drum, with the cords at an angle of about +60 and −60 degrees from the direction of travel, so they criss-crossed over each other. They were called cross-ply or bias ply tires. The plies were turned up around the steel wire beads and the combined tread/sidewall applied. The green (uncured) tire was loaded over a curing bladder and shaped into the mold. This shaping process caused the cords in the tire to assume an S shape from bead to bead. The angle under the tread stretched down to about 36 degrees. This was called the Crown Angle. In the sidewall region the angle was 45 degrees and in the bead it remained at 60 degrees. The low crown angle gave rigidity to support the tread and the high sidewall angle gave comfort.
By comparison, radial tires lay all of the cord plies at 90 degrees to the direction of travel (that is, across the tire from lip to lip). This design avoids having the plies rub against each other as the tire flexes, reducing the rolling friction of the tire. This allows vehicles with radial tires to achieve better fuel economy than vehicles with bias-ply tires. It also accounts for the slightly "low on air" (bulging) look that radial tire sidewalls have, especially when compared to bias-ply tires