The reason a human bite is usually worse than an animal bite is the human mouth can contain bacteria worse than a dogs mouth that can infect the person who has been bitten by the human.
You're less likely to get infected with any bacteria from a dogs bite to your human skin than you would if a human biting you.
Animal bites however can be much worse than a human bite though because an animal may be able to bite through your skin with more force than a human could.
For example a dog could likely maul your face and kill you while a human would be unlikely to bite hard enough to kill you by mauling you.
Dogs such as Pit Bull dogs could cause serious damage to a human and especially a baby, toddler or young kid.
So in that case the dog bite would be much worse than a human bite.
Also dogs can carry rabies which can cause health issues with the human that they bite and could kill the human with rabies if you don't get a rabies shot.