I checked—and dogs are significantly more likely to be abused than cats.
By their nature and relationship to humans, dogs are intended to be submissive and obedient, to follow our commands, and to try to please us by doing so.
Humans—even seemingly well-adjusted ones—don’t handle power and authority with much grace even at the best of time.
I expect abusive authoritarian personality types are more likely to be dog owners.
Dogs, being larger and tougher than cats, and expected to be obedient—may get abused more just because they’re seen as able to take greater punishment, and that such abuse may be perceived as a legitimate means of training a dog.
Cats don’t share any of these conditions and expectations that dogs typically have.