Radial ATV tires will ride smoother and last longer than their bias counterparts.  They have a sidewall that is typically more flexible, thereby increasing the size (and available traction) of the contact patch or footprint.  Typically radials will not have quite as deep of lug, or be quite as wide, however they are more efficient in producing traction.  Radial tires are more expensive to produce than bias tires, but also have increased longevity and better ride quality.  In automotive tires, radials are the standard for essentially all tires produced.