My dentist will take me with no money. Will he be as good as another?

He may be generous. Almost every dentist does some charity care - often it is the very best dentists who have plenty of patients able to pay that gives her/him resources necessary to take some with no money. Good for you! poor quality dentists are often struggling so much that they can't afford to do charity care.
Compassion. Maybe your dentist is just being very compassionate. Many physicians and dentists will see people despite the fact that they don't get paid just out of a sense of compassion and social responsibility.