Some people would say that the answer really depends on whether you are a human or a dog.

If you are a human, you are more likely to become infected if you are bitten by another human than by a dog. 

This is not because a dog's mouth is cleaner than a human.   The main reason is that more germs live in a human mouth than in a dog's mouth.

Most of the germs that live in a dog's mouth won't harm humans, but are actually more harmful to other dogs.

This is because bacteria or germs usually has the most effect on the same species.  Dog germs are more harmful to dogs, and human germs are more harmful to humans.

However, a dog does carry dead animals in its mouth, drink out of the toilet, and clean itself with its own tongue.  A dog can also transfer rabies and other infections from a dog bite.  A dog's mouth has lots of bacteria, since its tongue is also its wash cloth and acts as its toilet paper.

So is a dog's mouth dirtier than a human mouth.   The answer is a definite, "yes".