They both abused, but Rice was abuse to hurt and degrade, Peterson was ignorant in thinking the old ways of disciplining children can still be used today.
My mom belted me when I was a kid, marks and blood all over my bare back, butt, and legs. Was she criminal, no, but abusive and ignorant, yes. She honestly thought the bible meant what it said "spare the rod spoil the child" and in the south in the African American culture it is very common even today.