Just to clarify your question it sounds like your referring to problem based and case based as separate things. They are typically used interchangeably. You are given a problem or case and have to come up with a solution and in the process must do research in several different areas and in the process learn the material that would normally be presented in a lecture format.
All schools are clinical based. You have to perform the skills in the clinic on real patients in order to become a dentist, there is no escaping it.
Most dental schools (at least the limited number I interviewed at) spend the first two years focusing on general knowledge and working in the sim lab while the last two years are spent almost exclusively in the clinic. Schools are usually described as either lecture based (the learning in the first two years is presented primarily in a lecture format) or problem/case based learning depending on the format for the initial years. I'm sure there are schools that deviate from this somewhat, but I have not visited them.
USC is well known for being a Problem Based (PBL) school. I know there are others and I've heard that some schools are starting to take a combined approach, but I can't provide much in the way of a list.
Just curious, are you interested in attending a PBL school or trying to avoid them altogether?